A boy has only dimes and quarters in his piggy bank. if he has 70 coins worth 12 dollars and 40 cents altogether, how many quarters does he have in his bank?

Let us bear in mind the equivalent value of these coins:

One dime = $0.10

One quarter = $0.25

Let x = number of dimes

y = number of quarters

Since the boy has 70 coins in total, we can say that:

x + y = 70 (can be written as x = 70 - y)

Since the boy has a total of $12.40, we can say that:

0.10x + 0.25y = 12.40

To solve this problem, we need to solve this system of equation. We have to substitute the value of x as written in the first equation (x = 70 - y)

0.10 (70 - y) + 0.25y = 12.40

7 - 0.10y + 0.25y = 12.40

0.15y = 5.40

y = 36

X = 70 - 36

X = 34

Therefore, the boys has 34 dimes and 36 quarters. To check our answer, we just have to check if his money would total $12.40.

34 dimes = $3.40

36 dimes = $9.00

Total $12.40

12.40 is the answer ...