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If the value of x quarters is equal to the value of

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by VJesus12 » Mon May 14, 2018 1:13 am
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If the value of x quarters is equal to the value of x + 32 nickels, x =
(nickel = 5 cents, quarter = 25 cents)

(A) 8
(B) 11
(C) 14
(D) 17
(E) 20

The OA is the option A.

What is the equation that helps me here? Could anyone give me some help? Thanks in advance.
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by Vincen » Mon May 14, 2018 2:14 am
Hello vjesus12.

Let's take a look at your question.

If the value of x quarters is equal to the value of x + 32 nickels, it implies that: $$x\cdot quartes=(x+32)\cdot nickels$$ Now, we substitute

- 1 nickel = 5 cents.
- 1 quarter = 25 cents.

Hence we get: $$25x=\left(x+32\right)\cdot5\ \ \ \ \left(cents\right)$$ $$25x=5x+160\ \ \ \ \left(cents\right)$$ $$20x=160\ \ \ \ \left(cents\right)$$ $$x=8\ \ \ \ \left(cents\right)$$ Hence, the correct answer is the option [spoiler](A)=8[/spoiler].

I hope it helps you.
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by [email protected] » Mon May 14, 2018 11:34 am
Hi VJesus12,

We're told that the value of X quarters is equal to the value of (X + 32) nickels. We're asked for the value of X. This question can be approached in a number of different ways, including by 'brute force' arithmetic.

The value of 1 quarter is the same as the total value of 5 nickels, so the ratio must equal 1:5....
1 quarter and 5 nickels --> difference = 4 coins
2 quarters and 10 nickels --> difference = 8 coins
3 quarters and 15 nickels --> difference = 12 coins
Etc.

Notice how the difference increases by 4 coins with each additional quarter. We're told that there are 32 MORE nickels than quarters, so that would be 8(4). Thus, there are 8 quarters and 40 nickels.

Final Answer: A

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by Jeff@TargetTestPrep » Tue May 15, 2018 3:42 pm
VJesus12 wrote:If the value of x quarters is equal to the value of x + 32 nickels, x =
(nickel = 5 cents, quarter = 25 cents)

(A) 8
(B) 11
(C) 14
(D) 17
(E) 20
We can create the equation:

25x = 5(x + 32)

5x = x + 32

4x = 32

x = 8

Answer: A

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