Question 273593
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:

<pre>
                  1.70 * x + 1.30 * y = 37.90
                  5.60 * x + 5.40 * y = 147.20
</pre>
multiply the first equation by 5.6 and multiply the second equation by 1.7 to get:

<pre>
                  9.52 * x + 7.28 * y = 212.24
                  9.52 * x + 9.18 * y = 250.24
</pre>
subtract the first equation from the second equation to get:

<pre>
                             1.9 * y = 38
</pre>
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:

<pre>
                  1.70 * x + 1.30 * y = 37.90
                  5.60 * x + 5.40 * y = 147.20
</pre>
substituting 20 for x and 7 for y, these equations become:

<pre>
                  1.70 * 7 + 1.30 * 20 = 37.90
                  5.60 * 7 + 5.40 * 20 = 147.20
</pre>
after simplification, these equations become:

<pre>
                  11.9 +  26 =  37.90
                  39.2 + 108 + 147.20
</pre>
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.