Let's make some variables to represent the cost of the tables and chairs.
Let x be equal to the cost of one chair
Let y be equal to the cost of one table
The total cost for 3 chairs and 2 tables is $17.
3x + 2y = 17
The total cost for 8 chairs and 4 tables is $37.
8x + 4y = 37
Now we have our system of equations.
Let's solve it.
3x + 2y = 17
8x + 4y = 37
We can cancel the y's very easily. Then it would just leave us with the x's.
Multiply the top equation by -2.
3x(-2) + 2y(-2) = 17(-2) =
-6x - 4y = -34
Then add the equations together.
-6x - 4y = -34
8x + 4y = 37
=
2x = 3
Then just divide both sides by 2.
x = 1.5
Substitute 1.5 into one of the equation. I'll pick 3x + 2y = 17
3(1.5) + 2y = 17 ; Start
4.5 + 2y = 17 ; Multiply 3 and 1.5 together
2y = 12.5 ; Subtract 4.5 from each side of the equation
y = 6.25 ; Divide both sides by the coefficient of y. Which 2
So, a chair costs $1.50 and a table costs $6.25.
Ratios are equivalent when that can be reduced or multiplied to be the same number.
Ex) 1:4 is the same as 2:8 or 4:16
10:20 is the same as 8:16 or 1:2
They are not equivalent if you can’t do this
Answer --> 40 : 320
1/9 x 360 = 40
8/9 x 360 = 320
