Question

Karen has $1.70 in coins. Karen has 8 coins, all of which are quarters or dimes.

So can someone help me with these 3 parts?

Answer 1

Karen has 6 quarters and 2 dimes

Explanation:

Let

x ----> the number of quarter coins Karen has

y ----> the number of dimes coins Karen has

Remember that

`1\ quarter=\$0.25\\1\ dime=\$0.10`

we know that

Equation that represent the amount of coins Karen has

`x+y=8`

isolate the variable y

`y=8-x` ----> equation A

Equation that represent the value of coins Karen has

`0.25x+0.10y=1.70` ----> equation B

Solve the system of equations by substitution

substitute equation A in equation B

`0.25x+0.10(8-x)=1.70`

solve for x

`0.25x+0.80-0.10x=1.70`

`0.25x-0.10x=1.70-0.80`

`0.15x=0.90`

`x=6`

Find the value of y

`y=8-x` ---->
`y=8-6=2`

therefore

Karen has 6 quarters and 2 dimes