Question

I have a box of nickels and dimes. When I counted the money, I was surprised to see that I have exactly $10. Then it occurred to me that if my nickels were dimes and my dimes were quarters, I would have $21.25. How many dimes and nickels are in my box?

Answer 1

Answer on Question #48172 – Math – Algebra

I have a box of nickels and dimes. When I counted the money, I was surprised to see that I have exactly $10. Then it occurred to me that if my nickels were dimes and my dimes were quarters, I would have $21.25. How many dimes and nickels are in my box?

Solution:

Nickle = 5 cents;

Dime = 10 cents;

Quarter = 25 cents;

In your box you have x of dimes and y of nickels. So we can make a system of equations:

$$\left\{ \begin{array}{l} 0.1x + 0.05y = 10 \\ 0.1y + 0.25x = 21.25 \end{array} \right\}^2 \Rightarrow \left\{ \begin{array}{l} 0.2x + 0.1y = 20 \\ 0.1y + 0.25x = 21.25 \end{array} \right. \quad (1)$$

Now we will subtract (1) from (2):

$$0.05x = 1.25 \Rightarrow x = 25$$

We will put this value in (1):

$$5 + 0.1y = 20 \Rightarrow 0.1y = 15 \Rightarrow y = 150$$

**Answer:** You have in the box 150 nickels and 25 dimes.

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