Question

kevin had 13 coins in his pocket . all of his coins are either dimes or quarters . when he emptied his pockets kevin found he had $2.05.how many dimes and quarters does he have .

Answer 1

Kevin has 8 dimes and 5 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

kevin had 13 coins in his pocket

Therefore,

number of dimes + number of quarters = 13

d + q = 13 ------ eqn 1

When he emptied his pockets kevin found he had $2.05

We frame a equation as:

number of dimes x Value of 1 dime + number of quarters x Value of 1 quarter = 2.05

$d \times 0.10 + q \times 0.25 = 2.05$

0.10d + 0.25q = 2.05 ----------- eqn 2

Let us solve eqn 1 and eqn 2,

From eqn 1,

d = 13 - q ------- eqn 3

Substitute eqn 3 in eqn 2

0.10(13 - q) + 0.25q = 2.05

1.3 - 0.10q + 0.25q = 2.05

0.15q = 0.75

Divide both sides of equation by 0.15

q = 5

Substitute q = 5 in eqn 3

d = 13 - 5

d = 8

Thus there are 8 dimes and 5 quarters