Question

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

Answer 1

Answer:

Karen has 6 quarters and 2 dimes

Step-by-step 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