Question

In his pocket, Hamid has $2.95 in dimes and quarters. If there are 16 coins in total, which system represents the number of dimes and quarters that Hamid has?

Answer 1

`d+q=16...(1)`

`0.10d+0.25q=2.95...(2)`

Explanation:

Let d represent number of dimes and q represent number of quarters.

We have been given that Hamid has 16 coins in his pocket. We can represent this information in an equation as:

`d+q=16...(1)`

We know that value of each dime is $0.10, so value of d dimes would be
`0.10d`.

We also know that value of each quarter is $0.25, so value of q quarters would be
`0.25q`.

We are also told that the value of all coins is $2.95. We can represent this information in an equation as:

`0.10d+0.25q=2.95...(2)`

Therefore, our required system of equation would be:

`d+q=16...(1)`

`0.10d+0.25q=2.95...(2)`

Answer 2

x=dimes y=quarters

0.1x + 0.25y = 2.95
x+y = 16

from the second equation, x = 16 - y and thus 0.1 (16-y) +0.25y = 2.95 ==> y=9. Finally, x + 9 = 16 ==> x=7

7 dimes, 9 quarters