Tom B. answered • 11/14/22
Experienced, Friendly, and Plain-Speaking Math Tutor
A good approach to word problems is to name a variable for each "unknown" (what you want to what to find out). We want to find out:
The cost to rent a chair, let's call that C
The cost to rent a table, let's call that T
Now create equations using those variables based on the words in the word problem:
7C + 9T = 80
5C + 3T = 34
Then you figure out the values of the variables that make both equations true.
The equations like this are called a "system of equations". If you have two unknowns, you need to two equations. We have that. There are two techniques for finding out the unknowns: Elimination or Substitution. You can use either technique:
Elimination: You get rid of one of the variables by 1) multiplying an equation by a number and/or 2) adding or subtracting the equations. Then you can figure out the values...
For this problem, you can multiply the second equation by 3 and then subtract them
7C + 9T = 80
15C + 9T = 102
and get:
8C = 22, so C = 11/4 or $2.75
Then you plug that number into either equation, it doesn't matter which one:
5(11/4) + 3T = 34. This gives T = 27/4 or $5.50.
Substitution: For one of the equations, use algebra to get one of the variables by itself on one side of the equation. Then substitute that into the other equation. Then figure out the numbers:
From the second equation 5C + 3T = 34, we can get C = (34 - 3T)/5. Plug that into the other equation
7((34 - 3T)/5) + 9T = 80, which gives T = 27/4 or $5.50.
Plug that into one of the equations, it doesn't matter which one:
5C + 3(27/4) = 34, which gives C = 11/4 or $2.75
Both techniques give the same answer.
