System of Equation

Question

Molly's Custom Kitchen Supplies sells handmade forks and spoons. It costs the store $1.70 to buy the
supplies to make a fork and $1.30 to buy the supplies to make a spoon. The store sells forks for $5.60
and spoons for $5.40. Last April Molly's Custom Kitchen Supplies spent $37.90 on materials for forks
and spoons. They sold the finished products for a total of $147.20. How many forks and how many
spoons did they make last April?

Answer 1

Hi Chris,

Let X = cost to make a fork

Let Y = cost to make a spoon

Given the information above, we can write the following

system of equations:

1.70X + 1.30Y = 37.90

5.60X + 5.40Y = 147.20

Now we can solve for X with the system of equations.

(-5.40)(1.70X + 1.30Y) = (-5.40)(37.90)

(1.30)(5.60X + 5.40Y) = (1.30)(147.20)

-----------------------------------------

-9.18X - 7.02Y = -204.66

7.28X + 7.02Y = 191.36

-----------------------------------------

-1.90X = -13.30

X = 7

-----------------------------------------

After substituting the value of X into the first equation,

we can solve for Y.

1.70(7) + 1.30Y = 37.90

11.90 + 1.30Y = 37.90

1.30Y = 37.90 - 11.90

1.30Y = 26

Y = 20

Last April, Molly's Custom Kitchen Supplies made 7 forks

and 20 spoons.