When shopping, Luc note that a stick of glue and three

Question

When shopping, Luc
note that a stick of glue
and three boxes of pencils
color cost $ 33.93, that
two sticks of glue and two
boxes of colored pencils
cost $ 23.90 and only three sticks
of glue and a box of pencils
of color cost $ 13.87.
How much did he pay if he
bought three sticks of glue and two
boxes of colored pencils?

Answer 1

We have 2 unknowns and 3 equations.

X is the glue stick and y is the box of colored pencils,

or specifically, their RESPECTIVE prices.

 

The 3 equations are:

X + 3y = 33.93

2x + 2y = 23.90

3x+y = 13.87

 

Multiplying the 1st equation by -2 and ADDING THAT to the second

equation:

-4y = -43.96

(Your job is to VERIFY this step and convince yourself)

 

DIviding both sides by -4:

y = 10.99

 

Solving the first equation for x:

x = 33.93 - 3y = 33.93 - 3(10.99)

             = 0.96

 

So the prices are:
x=0.96 for the glue stick and y = 10.99 for 1 box of colored pencils

 

Again, the check is left for you to verify and check 

that these prices do in fact work in those 3 equations.

(Yes, they do. I checked them. But YOU SHOULD TOO!!!)

 

FInally 3 glue sticks and 2 boxes of colored pencils shall

cost

3(0.99) + 2(10.99) = 24.95

x=

0.96 and y = 10.99