SOLUTION: Molly's Custom Kitchen Supplies sells handmade forks and spoons. It cost 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

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Molly's Custom Kitchen Supplies sells handmade forks and spoons. It cost 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      Log On


   

Question 273593: Molly's Custom Kitchen Supplies sells handmade forks and spoons. It cost 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?
Found 2 solutions by Theo, mananth:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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.









Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Molly's Custom Kitchen Supplies sells handmade forks and spoons. It cost 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?

fork-----------------------spoon-------------------- total
1.7-------------------------1.3---------------------37.90
5.6-------------------------5.40--------------------147.20

let the number of forks sold be x and number of spoons sold be y

Cost equation
1.7x+1.3y=37.90-------------1
Sales equation
5.6x+5.4y = 147.20------------2
Multiply equation 1 by 5.6 and equation 2 by 1.7

9.52x+7.28y=212.24------------1
9.52x+9.18y=250.24-------------2
subtract 2 from 1
-1.9y=-38
y=-38/-1.9
y=20 the number of spoons
substitute the value of x in equation 1
x=7 the number of forks