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



Click here to post comments

Join in and write your own page! It's easy to do. How? Simply click here to return to System of linear equations.



Tough algebra word problems

100 Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Math quizzes

 Recommended