Ccss.math.content.8.ee.c.8b sample question

1. Evelyn Learning Systems
CCSS.Math.Content.8.EE.C.8 Analyze and solve pairs of simultaneous linear equations.
CCSS.Math.Content.8.EE.C.8c Solve real-world and mathematical problems leading to
two linear equations in two variables.
Question:
Write a system of equations to describe the situation below, solve using
elimination, and fill in the blanks.
A five-day fund raising event is being held at the city center. Yesterday, the
organizers sold 45 tables and 30 chairs, raising $1,350. Today, they were
able to sell 40 tables and 28 chairs, raising $1,220. How much do the
different pieces of furniture cost?
A table costs $ and a chair costs $
Hint:
To solve using the method of elimination, follow these four steps:
Step 1: Ensure the equations have either the x terms or y terms with
opposite signs.
Step 2: Add the two equations to eliminate one variable and solve for the
other.
Step 3: Put the result of Step 2 into one of the original equations and solve.
Step 4: State the solution.
Solution:
Before you can solve, you must write a system of equations.
Let x = the cost of a table, and let y = the cost of a chair.
45x + 30y = 1,350
40x + 28y = 1,220
Now use elimination to solve the system of equations.

2. Evelyn Learning Systems
Step 1: Make sure the equations have opposite x terms or opposite y terms.
Currently, neither the x terms (45x and 40x) nor the y terms (30y and 28y)
are opposites. Use multiplication to rewrite the equations with either
opposite x terms or opposite y terms. One good approach is to multiply the
first equation by 8 and the second equation by -9.
8(45x + 30y = 1,350) → 360x + 240y = 10,800
-9(40x + 28y = 1,220) → -360x – 252y = -10,980
Now the x terms (360x and -360x) are opposites.
Step 2: Add the equations to eliminate one variable and solve for the other.
Add to eliminate the x terms, and then solve for y.
360x + 240y = 10,800
+ (-360x – 252y = -10,980)
0x – 12y = -180 Add to eliminate the x terms
-12y = -180 Simplify
y = 15 Divide both sides by -12
Step 3: Put the result of Step 2 into one of the original equations and solve.
Take the result of Step 2, y = 15, and put it into one of the original
equations, such as 45x + 30y = 1,350. Then find the value of x.
45x + 30y = 1,350
45x + 30 (15) = 1,350 Put in y = 15

3. Evelyn Learning Systems
45x + 450 = 1,350 Multiply
45x = 900 Subtract 450 from both sides
x = 20 Divide both sides by 45
Step 4: State the solution.
Since x = 20 and y = 15, the solution is (20, 15).
A table costs $20, and a chair costs $15.