et 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.