let x = number of forks
let y = number of spoons
cost of a fork = 1.70
cost of a spoon = 1.30
revenue from a fork = 5.60
revenue from a spoon = 5.40
In april they spent 37.90 on material.
They sold them for a total of 147.20
your cost equation is:
1.70 * x + 1.30 * y = 37.90
your revenue equation is:
5.60 * x + 5.40 * y = 147.20
solve these two equations simultaneously to get your answer.
simultaneously means the same value of x and the same value of y solve both equations at the same time.
your two equations are:
1.70 * x + 1.30 * y = 37.90
5.60 * x + 5.40 * y = 147.20
multiply the first equation by 5.6 and multiply the second equation by 1.7 to get:
9.52 * x + 7.28 * y = 212.24
9.52 * x + 9.18 * y = 250.24
subtract the first equation from the second equation to get:
1.9 * y = 38
divide both sides of this equation by 1.9 to get:
y = 20
substitute that value for y in the first original equation.
first original equation is:
1.70 * x + 1.30 * y = 37.90
substitute 20 for y to get:
1.70 * x + 1.30 * 20 = 37.90 which becomes:
1.70 * x + 26 = 37.90
subtract 26 from both sides of this equation to get:
1.70 * x = 37.90 - 26 which becomes:
1.70 * x = 11.90
divide both sides of this equation by 1.7 to get:
x = 11.90 / 1.7 = 7
you have:
x = 7
y = 20
substitute these values into the original equations to confirm they are good.
the original equations are:
1.70 * x + 1.30 * y = 37.90
5.60 * x + 5.40 * y = 147.20
substituting 20 for x and 7 for y, these equations become:
1.70 * 7 + 1.30 * 20 = 37.90
5.60 * 7 + 5.40 * 20 = 147.20
after simplification, these equations become:
11.9 + 26 = 37.90
39.2 + 108 + 147.20
both equations are true so the value for x and y are good.
those values are:
x = 7
y = 20
they made 7 forks and 20 spoons.