Question

You save dimes and quarters in a cup in your locker. When you count them, you find that you have 20 coins with a value of $3.20. How many of each type of coin do you have?
A. 10 dimes and 10 quarters
B. 14 dimes and 6 quarters
C. 12 dimes and 8 quarters
D. 8 dimes and 12 quarters

Answer 1

how much is a dime worth?

Answer 2

how much is a quarter worth?

Answer 3

say that we call x the number of dimes and y the number of quarters.

Answer 4

is it b? @tomo

Answer 5

.1x + .25y = $3.20

Answer 6

x+y = 20

Answer 7

solve the system of equations.

Answer 8

D. thank you @tomo

Answer 9

let

d = # of dimes
q = # of quarters


The first equation is

d+q = 20

since you have 20 coins total

Solve for q to get

q = 20 - d

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Total value of all coins is $3.20, which means

0.10d + 0.25q = 3.20

10d + 25q = 320 ... Multiply both sides of the last equation above by 100 to clear out the decimals.


Now plug in q = 20 - d to get

10d + 25q = 320

10d + 25(20 - d) = 320

10d + 500 - 25d = 320

Solve that for d

Once you have the value of d, plug it into q = 20 - d to find the value of q. I'll let you do this.