Solving a word problem with 3 unknowns using a linear equation

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