Algebra, NAPX-E4-CA24 SA

Question

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Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

698

Question

Jim and Andy each bought a large order of plums from the farmers' market.

Jim bought three-quarters of the quantity that Andy bought.

The total cost of Jim and Andy's plums was $158.55.

What was the cost of Andy's plums?

Worked Solution
Let  a\ \large a = cost of Andy's plums
34a\dfrac{3}{4} \large a = cost of Jim's plums

a\large a + 34a\dfrac{3}{4} \large a = 158.55
74a\dfrac{7}{4}\large a = 158.55
∴a\therefore \large a = 158.55 ÷ 74\div \ \dfrac{7}{4}
= $90.60

Question Type

Answer Box

Variables

Variable nameVariable value
question
Jim and Andy each bought a large order of plums from the farmers' market. Jim bought three-quarters of the quantity that Andy bought. The total cost of Jim and Andy's plums was $158.55. What was the cost of Andy's plums?
workedSolution
| | | | ------------: | ---------- | | Let $\ \large a$ | \= cost of Andy's plums | | $\dfrac{3}{4} \large a$ | \= cost of Jim's plums |

| | | | ------------: | ---------- | | $\large a$ + $\dfrac{3}{4} \large a$ | \= 158.55 | | $\dfrac{7}{4}\large a$ | \= 158.55 | | $\therefore \large a$ | \= 158.55 $\div \ \dfrac{7}{4}$ | | | \= {{{prefix0}}}{{{correctAnswer0}}} |
correctAnswer0
90.60
prefix0
$
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer090.60

$

Variant 1

DifficultyLevel

701

Question

Bob and Chris each bought a large order of nails from the hardware store.

Bob bought four fifths of the quantity that Chris bought.

The total cost of Bob and Chris's nails was $62.55.

What was the cost of Chris's nails?

Worked Solution
Let  c\ \large c = cost of Chris's nails
45c\dfrac{4}{5} \large c = cost of Bob's nails

c\large c + 45c\dfrac{4}{5} \large c = 62.55
95c\dfrac{9}{5}\large c = 62.55
∴c\therefore \large c = 62.55 ÷ 95\div \ \dfrac{9}{5}
= $34.75

Question Type

Answer Box

Variables

Variable nameVariable value
question
Bob and Chris each bought a large order of nails from the hardware store. Bob bought four fifths of the quantity that Chris bought. The total cost of Bob and Chris's nails was $62.55. What was the cost of Chris's nails?
workedSolution
| | | | ------------: | ---------- | | Let $\ \large c$ | \= cost of Chris's nails | | $\dfrac{4}{5} \large c$ | \= cost of Bob's nails |

| | | | ------------: | ---------- | | $\large c$ + $\dfrac{4}{5} \large c$ | \= 62.55 | | $\dfrac{9}{5}\large c$ | \= 62.55 | | $\therefore \large c$ | \= 62.55 $\div \ \dfrac{9}{5}$ | | | \= {{{prefix0}}}{{{correctAnswer0}}} |
correctAnswer0
34.75
prefix0
$
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer034.75

$

Variant 2

DifficultyLevel

700

Question

Sally and Greta own adjoining blocks of land.

Sally's land is five-eighths the size of Greta's.

The combined area of Sally and Greta's land is 3380 square metres.

What is the area of Greta's block in square metres?

Worked Solution
Let  g\ \large g = area of Greta's land
58g\dfrac{5}{8} \large g = area of Sally's land

g\large g + 58g\dfrac{5}{8} \large g = 3380
138g\dfrac{13}{8}\large g = 3380
∴g\therefore \large g = 3380 ÷ 138\div \ \dfrac{13}{8}
= 2080 square metres

Question Type

Answer Box

Variables

Variable nameVariable value
question
Sally and Greta own adjoining blocks of land. Sally's land is five-eighths the size of Greta's. The combined area of Sally and Greta's land is 3380 square metres. What is the area of Greta's block in square metres?
workedSolution
| | | | ------------: | ---------- | | Let $\ \large g$ | \= area of Greta's land | | $\dfrac{5}{8} \large g$ | \= area of Sally's land |

| | | | ------------: | ---------- | | $\large g$ + $\dfrac{5}{8} \large g$ | \= 3380 | | $\dfrac{13}{8}\large g$ | \= 3380 | | $\therefore \large g$ | \= 3380 $\div \ \dfrac{13}{8}$ | | | \= {{{correctAnswer0}}} {{{suffix0}}} |
correctAnswer0
2080
prefix0
suffix0
square metres

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer02080

square metres

Variant 3

DifficultyLevel

694

Question

Bert and Ernie each bought a large order of cookies from the supermarket.

Bert bought two-thirds of the quantity that Ernie bought.

The total cost of Bert and Ernie's cookies was $64.50.

What was the cost of Ernie's cookies?

Worked Solution
Let  e\ \large e = cost of Ernie's cookies
23e\dfrac{2}{3} \large e = cost of Bert's cookies

e\large e + 23e\dfrac{2}{3} \large e = 64.50
53e\dfrac{5}{3}\large e = 64.50
∴e\therefore \large e = 64.50 ÷ 53\div \ \dfrac{5}{3}
= $38.70

Question Type

Answer Box

Variables

Variable nameVariable value
question
Bert and Ernie each bought a large order of cookies from the supermarket. Bert bought two-thirds of the quantity that Ernie bought. The total cost of Bert and Ernie's cookies was $64.50. What was the cost of Ernie's cookies?
workedSolution
| | | | ------------: | ---------- | | Let $\ \large e$ | \= cost of Ernie's cookies | | $\dfrac{2}{3} \large e$ | \= cost of Bert's cookies |

| | | | ------------: | ---------- | | $\large e$ + $\dfrac{2}{3} \large e$ | \= 64.50 | | $\dfrac{5}{3}\large e$ | \= 64.50 | | $\therefore \large e$ | \= 64.50 $\div \ \dfrac{5}{3}$ | | | \= {{{prefix0}}}{{{correctAnswer0}}} |
correctAnswer0
38.70
prefix0
$
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer038.70

$

Variant 4

DifficultyLevel

702

Question

Kramer and Elaine each bought a large order of soup from the soup kitchen.

Kramer bought four-ninths of the quantity that Elaine bought.

The total cost of Kramer and Elaine's soup was $72.93.

What was the cost of Elaine's soup?

Worked Solution
Let  e\ \large e = cost of Elaine's soup
49e\dfrac{4}{9} \large e = cost of Kramer's soup

e\large e + 49e\dfrac{4}{9} \large e = 72.93
139e\dfrac{13}{9}\large e = 72.93
∴e\therefore \large e = 72.93 ÷ 139\div \ \dfrac{13}{9}
= $50.49

Question Type

Answer Box

Variables

Variable nameVariable value
question
Kramer and Elaine each bought a large order of soup from the soup kitchen. Kramer bought four-ninths of the quantity that Elaine bought. The total cost of Kramer and Elaine's soup was $72.93. What was the cost of Elaine's soup?
workedSolution
| | | | ------------: | ---------- | | Let $\ \large e$ | \= cost of Elaine's soup | | $\dfrac{4}{9} \large e$ | \= cost of Kramer's soup |

| | | | ------------: | ---------- | | $\large e$ + $\dfrac{4}{9} \large e$ | \= 72.93 | | $\dfrac{13}{9}\large e$ | \= 72.93 | | $\therefore \large e$ | \= 72.93 $\div \ \dfrac{13}{9}$ | | | \= {{{prefix0}}}{{{correctAnswer0}}} |
correctAnswer0
50.49
prefix0
$
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer050.49

$

Variant 5

DifficultyLevel

698

Question

April and May buy their coffee beans from the local cafe.

Last month, April bought three-eighths of the quantity of coffee beans that May bought.

The total cost of April and May's coffee beans last month was $107.80.

What was the cost of May's coffee beans over this time?

Worked Solution
Let   m\ \large m = cost of May's coffee beans
38m\dfrac{3}{8} \large m = cost of April's coffee beans

m\large m + 38m\dfrac{3}{8} \large m = 107.80
118m\dfrac{11}{8}\large m = 107.80
∴m\therefore \large m = 107.80 ÷ 118\div \ \dfrac{11}{8}
= $78.40

Question Type

Answer Box

Variables

Variable nameVariable value
question
April and May buy their coffee beans from the local cafe. Last month, April bought three-eighths of the quantity of coffee beans that May bought. The total cost of April and May's coffee beans last month was $107.80. What was the cost of May's coffee beans over this time?
workedSolution
| | | | ------------: | ---------- | | Let  $\ \large m$ | \= cost of May's coffee beans | | $\dfrac{3}{8} \large m$ | \= cost of April's coffee beans |

| | | | ------------: | ---------- | | $\large m$ + $\dfrac{3}{8} \large m$ | \= 107.80 | | $\dfrac{11}{8}\large m$ | \= 107.80 | | $\therefore \large m$ | \= 107.80 $\div \ \dfrac{11}{8}$ | | | \= {{{prefix0}}}{{{correctAnswer0}}} |
correctAnswer0
78.40
prefix0
$
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer078.40

$

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