Question 13 options:
a jar contains 50 coins, all of which are dimes and quarters.

the total value of the coins in the jar is $7.70.

how many dimes/quarters are in the jar?

The jar has 32 dimes and 18 quarters

Step-by-step explanation:

To solve this problem we can create a system of linear equations in terms of two-variables (say and ) and solve it. To begin let us analyze the problem further. We know that the values of each coin type are:

Dimes ( )     = $0.10

Quarters( )  = $0.25

Total Value   = $7.70

Total Coins   = 50

Now let us set up our system of equations as:

     Eqn.(1)

                    Eqn.(2)

Lets take Eqn.(2) and rerrange it to solve for as:

                    Eqn.(3)

Now lets plug this, in Eqn.(1) so we get the value of as:

Plugging in back in Eqn.(3) we finally have:

Thus we conclude that in the jar the coins are:

Dimes ( )

Quarters( )