Amanda, Henry, and Scott have a total of $89 in their wallets. Amanda has $6 less than Scott. Henry has 3 times what Scott has. How much does each have?
Solution
Let x be the amount of money Amanda has
Let y be the amount of money Henry has
Let z be the amount of money Scott has
Amanda, Henry, and Scott have a total of $89 in their wallets.
The above statement gives the following equation
x + y + z = 89
Amanda has $6 less than Scott
The above statement gives the following equation
x = z - 6
Henry has 3 times what Scott has.
The above statement gives the following equation
y = 3z
We get the following 3 equations
x + y + z = 89 equation 1
x = z - 6 equation 2
y = 3z equation 3
Replace x = z - 6 and y = 3z in equation 1
z - 6 + 3z + z = 89
5z - 6 = 89
5z - 6 + 6 = 89 + 6
5z = 95
Divide both sides by 5
5z/ 5 = 95 / 5
z = 19
Scott has 19 dollars
y = 3z = 3 × 19 = 57
Henry has 57 dollars
z - 6 = x
19 - 6 = x
13 = x
Amanda has 13 dollars
Jan 26, 23 11:44 AM
Jan 25, 23 05:54 AM