At a certain fruit stand, the price of an apple is twice the price of an

At a certain fruit stand, the price of an apple is twice the price of an orange. For which of the following combinations of apples and oranges is the total price equal to the total price of $20$ oranges?

Indicate all such combinations

  1. $2$ apples and $16$ oranges
  2. $3$ apples and $14$ oranges
  3. $4$ apples and $10$ oranges
  4. $6$ apples and $8$ oranges
  5. $10$ apples and $5$ oranges
  6. $12$ apples and $4$ oranges

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 11 of the second Quantitative section 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.

Here we’re given a math equation, in words, relating the price of apples and oranges. Then we’re asked to find expressions equivalent in price to $20$ oranges. Questions that give us math equations as sentences and then ask us to find equivalence between different expressions are usually going to test our Solving Linear Equations ability. 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. An apple costs twice as much as an orange
  2. We want to know which combinations of fruits have the same cost as $20$ oranges

 

Develop a Plan

We want to know which of these fruit combinations is equal in price to $20$ oranges. One strategy we could use is to convert all of the answer choices to their equivalent cost in ONLY oranges, and then see if we have $20$ oranges for that answer choice.

Since an apple costs twice as much as an orange, we can convert the price of apples to the price of oranges by multiplying the number of apples by $2$. Then if we add in the number of oranges…presto! We’ll have the equivalent costs of that fruit combination, but just with oranges. So for example, if we had $1$ apple and $18$ oranges, we’d do: $1·2+18 = 2+18=20$. So $1$ apple and $18$ oranges costs the same amount as $20$ oranges. Let’s use this method to check each answer choice.

Solve the Question

So for each answer choice, we’ll multiply the number of apples by $2$ and add it to the number of oranges. Correct answers should give us the value $20$.

Check A: $2$ apples and $16$ oranges

$$2·2+16=4+16=20$$

A is correct. Let’s check B.

Check B: $3$ apples and $14$ oranges

$$2·3+14=6+14=20$$

B is correct. Let’s check C.

Check C: $4$ apples and $10$ oranges

$$2·4+10=8+10=18$$

Ah, C is incorrect, as it’s only equivalent to the cost of $18$ oranges. Let’s check D.

Check D: $6$ apples and $8$ oranges

$$2·6+8=12+8=20$$

D is correct. Let’s check E.

Check E: $10$ apples and $5$ oranges

$$2·10+5=20+5=25$$

Ah, E is incorrect, as it’s equivalent to the cost of $25$ oranges. Let’s check F.

Check F: $12$ apples and $4$ oranges

$$2·12+4=24+4=28$$

Ah, F is incorrect, as it’s equivalent to the cost of $28$ oranges.

The correct answer is A, B, and D.

What Did We Learn

Though we could have assumed a certain cost per orange and then calculated the monetary value of each answer choice,
it was much more convenient to think of this question from the perspective of changing one apple into two oranges, and then comparing the total number of oranges to the value of $20$.

 

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