+3 Tobys piggy bank contains only 5c and 10c coins. If it contains 65 coins with a total value of $3.80, find the number of each type of coin. Let x and y be the number of 5c and 10c coins respectively. Use the fact that the total number of coins is 65 to set up equation 1. Write the equation in the form ax+by=c
+128475 x + y = 65 ⇒ y = 65 - x (1)
5x + 10y = 380 (2)
Sub (1) into (2) for y and we have that
5x + 10 ( 65 - x) = 380 simplify
5x + 650 - 10x = 380
-5x + 650 = 380 subtract 650 from each side
-5x = -270 divide both sides by -5
x = 54 = the number of 5 cent coins
And 65 - x = 65 - 54 = 11 = the number of 10 cent coins
+9466 The total number of coins is 65
x + y = 65 ←This is equation 1
The total value of the coins is $3.80
the total number of cents = 380
5x + 10y = 380 ←This is equation 2
From equation 1 we know...
x + y = 65
x = 65 - y
From equation 2 we know...
5x + 10y = 380
We know x = 65 - y so we can substitute 65 - y in for x
5( 65 - y ) + 10y = 380
Distribute 5 to the terms in parenthesees.
325 - 5y + 10y = 380
Subtract 325 from both sides.
-5y + 10y = 380 - 325
Combine like terms.
5y = 55
Divide both sides by 5
y = 11
Again from equation 1 we know....
x = 65 - y
And we just determined that y = 11
x = 65 - 11
x = 54
