Shannon had a total of twenty dimes and quarters. If the value of the coins was $3.35, how many...?

Question

of each coin did she have?

Answer 1

x(.1) + 20-x(.25) = 3.35

.1x + 5 - .25x = 3.35

-.15x = -1.65

x= 11 (dimes)

Answer 2

Here's the way I've always done it, which doesn't get entrenched in the math symbols:

Twenty dimes would give us $2.00.

For each dime we exchange for a quarter, we gain $0.15.  Since we need to gain a total of $1.35, we need to get 1.35/.15 = 9 quarters.

This leaves us with 20-9 = 11 dimes.

To summarize:

11 dimes, 9 quarters.

Answer 3

11 dimes and 9 quarters  

Answer 4

11 dimes (110 cents) and 9 quarters (225 cents)

Answer 5

11 dimes and 9 quarters makes $3.35

Answer 6

d = dimes

q = quarters

total coins = 20

d + q = 20

0.10d + 0.25q = 3.35

Solve the system of equations by process of elimination:

Multiply the first equation by -0.10 and add the result to the second equation:

-0.10d + -0.10q = -2

+0.10d + 0.25q = 3.35

-------------------------------

0.15q = 1.35

q = 9

Now, use q=9 to solve for d in the first equation:

d + q = 20

d + 9 = 20

d = 11

Check:

0.10(11) + 0.25(9) = 3.35

1.10 + 2.25 = 3.35

So, therefore

d = 11, q = 9