I've got 58 coins that add up to $9.40. If the coins are only quarters and dimes how many of each do I have?

Answer 1

Let's use the variable d to represent the NUMBER of dimes and the variable q represent the NUMBER of quarters.

Since there are a total of 58 coins, we can write the following equation: d + q = 58

Then since each dime is worth $0.10 and each quarter is worth $0.25 with a total of $9.40, we can write the following equation: 0.10 d + 0.25 q = 9.40

Now we can solve these two equations in two unknowns using elimination:

d + q = 58

0.10 d + 0.25 q = 9.40

Multiply the first equation by -0.10 to eliminate the variable d and solve for q:

-0.10 d + -0.10 q = -5.80

0.10 d + 0.25 q = 9.40

0.15 q = 3.60

q = 24

You will have 24 quarters.

Since there are a total of 58 coins , you will have 34 dimes (24 + 34 = 58).

To verify:

$0.10 * 34 + $0.25 * 24 = $3.40 + 6.00 = $9.40