A total of 95 coins quarters and dimes;the total is $15.35; how many dimes ?

Answer 1

If we let q represent number of quarters and d represent number of dimes, we can come up with two equations:

q + d = 95 (the total number of coins we have is 95)

0.25q + 0.10d = 15.35 (the .25 and .10 come from the monetary worth of quarters and dimes)

From there, we can solve one of the equations for one variable and substitute that in the second equation. For simplicity, let's solve the first equation for q.

By subtracting d from both sides, we end up with q = 95 - d. Let's plug that into our second equation.

0.25(95 - d) + 0.10d = 15.35

23.75 - 0.25d + 0.10d = 15.35 (distributive property)

23.75 - 0.15d = 15.35 (combine like terms)

-0.15d = -8.40 (subtract 23.75 from both sides)

d = 56 (divide both sides by -0.15)

From this we can see that we have 56 dimes. Going back to our first equation, we can then solve for how many quarters we have.

q + d = 95

q + 56 = 95

q = 39

So, we have 56 dimes and 39 quarters.

If you want to double check your work, we can see that 0.25(39) + 0.10(56) does in fact equal 15.35.

Answer 2

Let q be the total number of quarters, and d be the total number of dimes

This means our first equation detailing the total number of coins is

q + d = 95

Our second equation details the amount of money

0.25q + 0.10d = 15.35

(we use 0.25 and 0.10 because those are the values of a quarter and a dime)

Subtracting q from both sides in the first equation, we get

d = 95-q

We can plug this into the second equation, giving us

0.25q + 9.5-0.1q = 15.35

0.15q = 5.85

q = 39

Therefore, d = 95 - 39 = 56

Therefore, we have 39 quarters and 56 dimes