Randall has 34 coins in his pocket, all of which are dimes and quarters. If the total value of his change is 625 cents, how many dimes and how many quarters does he have?

Answer 1

For a system of equations we could use one for the total number of coins and one for the total value of the coins

Equation 1 for the total number of coins

x + y = 34

Equation 2 for total value of the coins

10x + 25y = 625 cents

If we multiply Equation 1 by negative 10 we have

-10(x + y = 34)

-10x - 10y = -340

We can add this to Equation 2

10x + 25y = 625

-10x - 10y = -340

We get

15y = 285

Divide both sides of the equation by 15

y = 19

Substitute this into = Equation 2 to find x

10x + 25(19) = 625

10x +475 = 625

Subtract 475 from both sides

10x = 150

Divide both sides by 10

x = 15

We check these values in the equations

x = 15

y = 19

15 + 19 = 34

10(15) + 25(19) = 625

150 + 475 = 625

Substitution also works for this system of equations, in Equation 1

x + y = 34

y = 34 -x

You can substitute this quantity for y in Equation 2

10x + 25y = 625

10x + 25(34 - x) = 625

10x + 850 - 25x = 625

Combine like terms

-15x + 850 = 625

Subtract 850 from both sides of the equation

-15x = 625- 850

-15x = -225

Divide both sides by -15

x = 15

Now go back and solve for y

Give it a try.

If you have any questions please send me a message.