Question

Jada told Noah that she has $2 worth of quarters

and dimes in her pocket and 17 coins all together.
She asked him to guess how many of each type of
coin she has.​

Answer 1

Jadah has 15 dimes and 2 quarters

Solution:

Let "d" be the number of dimes

Let "q" be the number of quarters

We know that,

value of 1 dime = $ 0.10

value of 1 quarter = $ 0.25

She has 17 coins altogether

number of dimes + number of quarters = 17

d + q = 17 ----- eqn 1

She has $2 worth of quarters and dimes in her pocket

number of dimes x value of 1 dime + number of quarters x value of 1 quarter = 2

`d * 0.10 + q * 0.25 = 2`

0.1d + 0.25q = 2 ---- eqn 2

Let us solve eqn 1 and eqn 2

From eqn 1,

d = 17 - q ------- eqn 3

Substitute eqn 3 in eqn 2

0.1(17 - q) + 0.25q = 2

1.7 - 0.1q + 0.25q = 2

0.15q = 0.3

q = 2

From eqn 3,

d = 17 - q = 17 - 2 = 15

d = 15

Thus she has 15 dimes and 2 quarters