George has 52 coins in quarters and nickels. He has a total of $3.60. How many quarters does he have?

there are 36 quarters.

Let the number of nickels be x

Let the number of quarters be y

Value Value

Type Number of of

of of EACH ALL

coin coins coin coins

nickels x $0.05 $0.05x

quarters y $0.25 $0.25y

TOTALS 52 $3.60

The first equation comes from the second column.

x + y = 11

The second equation comes from the last column.

0.05x + 0.25y = 3.60

Get rid of decimals by multiplying every term by 100:

5x + 25y = 360

So we have the system of equations:

x+y=52

5x+25y=360

We solve by substitution. Solve the first equation for y:

x + y = 52

y = 52 - x

Substitute (52 - x) for y in 5x + 25y = 360

5x + 25(52 - x) = 360

5x + 1300 - 25x = 360

-20x + 1300 = 360

-20x = -940

x = = 5 the number of nickels.

Substitute in y = 52 - x

y = 52 - (5

y = 47 quarters.

The number of quarters is 52-x or 52-5 or 47 quarters.

answer for #1 is c

answer for #2 is d

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step-by-step explanation: