solving a word problem with 3 unknowns using a linear equation

Amanda, Henry, and Scott have a total of \$89 in thier 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 thier
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

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