A fruit stand sells two varieties of apples at $1.00 and $1.25 per pound

A fruit stand sells two varieties of apples at $\$1.00$ and $\$1.25$ per pound, respectively, and two varieties of oranges at $\$1.25$ and $\$1.50$ per pound, respectively. Which of the following could be the total price of $3$ pounds of one variety of apples and $2$ pounds of one variety of oranges at the stand?

Indicate all such prices.

  1. $\$5.75$
  2. $\$6.00$
  3. $\$6.25$
  4. $\$6.50$
  5. $\$6.75$

So, you were trying to be a good test taker and practice for the GRE with PowerPrep online. Buuuut then you had some questions about the quant section—specifically question 20 of Section 6 of Practice Test 1. Those questions testing our knowledge of Solving Linear Equations can be kind of tricky, but never fear, PrepScholar has got your back!

Survey the Question

Let’s search the problem for clues as to what it will be testing, as this will help shift our minds to think about what type of math knowledge we’ll use to solve this question. Pay attention to any words that sound math-specific and anything special about what the numbers look like, and mark them on our paper.

Well, besides making us hungry for fruit, this question seems to give us words that we can translate into math equations, which we can then use to solve this question. So sounds like we’ll draw upon our Solving Linear Equations math ability here. Let’s keep what we’ve learned about this skill at the tip of our minds as we approach this question.

What Do We Know?

Let’s carefully read through the question and make a list of the things that we know.

 

  1. We have two varieties of apples that cost $\$1.00$ and $\$1.25$ per pound, respectively
  2. We have two varieties of oranges that cost $\$1.25$ and $\$1.50$ per pound, respectively
  3. We want to know the possible values for the cost of $3$ pounds of apples and $2$ pounds of oranges together

 

Develop a Plan

In the end, we’re looking for the total cost of the fruit, which we know we can get if we multiply the cost per pound by the number of pounds for the fruit:

$$\Cost = \Cost \per \Pound · \Number \of \Pounds$$

We have two varieties of apples, which we can call $\Apples_1$, which cost $\$1.00$ per pound, and $\Apples_2$, which cost $\$1.25$ per pound. We also have two varieties of oranges, which we can call $\Oranges_1$, which cost $\$1.25$ per pound, and $\Oranges_2$, which cost $\$1.50$ per pound. We want to combine $3$ pounds of apples and $2$ pounds of oranges, for which we can see four different ways that we can accomplish this.

  1. $3$ pounds of $\Apples_1$ and $2$ pounds of $\Oranges_1$
  2. $3$ pounds of $\Apples_1$ and $2$ pounds of $\Oranges_2$
  3. $3$ pounds of $\Apples_2$ and $2$ pounds of $\Oranges_1$
  4. $3$ pounds of $\Apples_2$ and $2$ pounds of $\Oranges_2$

So let’s plan to find the total cost for each of these four scenarios. We’ll keep track of them and at the end select whichever answer choices match up with what we calculated.

Solve the Question

Scenario 1: $3$ pounds of $\Apples_1$ and $2$ pounds of $\Oranges_1$

With $3$ pounds of apples that cost $\$1.00$ per pound and $2$ pounds of oranges that cost $\$1.25$ per pound, we get:

$\Total \Cost$ $=$ $3·\Apples \Cost \per \Pound + 2·\Oranges \Cost \per \Pound$
$ $ $ $
$\Total \Cost$ $=$ $3·\$1.00 + 2·\$1.25$
$ $ $ $
$\Total \Cost$ $=$ $\$3.00 + \$2.50$
$ $ $ $
$\Total \Cost$ $=$ $\$5.50$

Scenario 2: $3$ pounds of $\Apples_1$ and $2$ pounds of $\Oranges_2$

With $3$ pounds of apples that cost $\$1.00$ per pound and $2$ pounds of oranges that cost $\$1.50$ per pound, we get:

$\Total \Cost$ $=$ $3·\Apples \Cost \per \Pound + 2·\Oranges \Cost \per \Pound$
$ $ $ $
$\Total \Cost$ $=$ $3·\$1.00 + 2·\$1.50$
$ $ $ $
$\Total \Cost$ $=$ $\$3.00 + \$3.00$
$ $ $ $
$\Total \Cost$ $=$ $\$6.00$

Scenario 3: $3$ pounds of $\Apples_2$ and $2$ pounds of $\Oranges_1$

With $3$ pounds of apples that cost $\$1.25$ per pound and $2$ pounds of oranges that cost $\$1.25$ per pound, we get:

$\Total \Cost$ $=$ $3·\Apples \Cost \per \Pound + 2·\Oranges \Cost \per \Pound$
$ $ $ $
$\Total \Cost$ $=$ $3·\$1.25 + 2·\$1.25$
$ $ $ $
$\Total \Cost$ $=$ $\$3.75 + \$2.50$
$ $ $ $
$\Total \Cost$ $=$ $\$6.25$

Scenario 4: $3$ pounds of $\Apples_2$ and $2$ pounds of $\Oranges_2$

With $3$ pounds of apples that cost $\$1.25$ per pound and $2$ pounds of oranges that cost $\$1.50$ per pound, we get:

$\Total \Cost$ $=$ $3·\Apples \Cost \per \Pound + 2·\Oranges \Cost \per \Pound$
$ $ $ $
$\Total \Cost$ $=$ $3·\$1.25 + 2·\$1.50$
$ $ $ $
$\Total \Cost$ $=$ $\$3.75 + \$3.00$
$ $ $ $
$\Total \Cost$ $=$ $\$6.75$

So the four possibilities are: $\$5.50, \$6.00, \$6.25, \and \$6.75$. This corresponds with the correct answer being B,
C, and D
.

What Did We Learn

Writing out equations and plugging in values definitely made this problem much more manageable than it initially appeared to be. Also, it was very wise of us to breakdown the four different scenarios and calculate the total cost for each one.
What started off as a monster-sized question quickly became easy to solve as four smaller questions.

 

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