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Kevin and Randy have a jar containing 67 coins all of which are either quarters or nickels. The total value of the coins in the jar $12.75 ... how many of each type of coin do they have?

Respuesta :

Answer:

47quarters and 20 nickel

Explanation:

Let the number of quarters be x

Let the number of nickels be y

If there are 67 coins in the jar, then;

x + y = 67 ....1

1 quarter = 0.25x

1 nickel = 0.05y

If the total value of the coins in the jar is $12.75, then;

0.25x + 0.05y = 12.75 ....2

Multiply through by 100

25x + 5y = 1275 ....2

Solve 1 and 2 simultaneously

x + y = 67 ....1 * 25

25x + 5y = 1275 ....2 * 1

Using Elimination method

________________________

25x + 25y = 1,675

25x + 5y = 1275

Subtract

25y - 5y = 1675 - 1275

20y = 400

y = 400/20

y = 20

Substitute y = 20 into equation 1;

From 1; x + y = 67

x + 20 = 67

x = 67 - 20

x = 47

This means there are 47quarters and 20 nickel.

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