SOLUTION: I know the "backward" way in getting the answer to this problem, but I create the formula for this problem: A restaurant owner wants to purchase some new tables, chairs and dinner

Question 78604: I know the "backward" way in getting the answer to this problem, but I create the formula for this problem:
A restaurant owner wants to purchase some new tables, chairs and dinner plates. She plans to buy four chairs and four plates for each table. Sh also needs 20 additional plates to keep for breakage. If a table costs $100, a chair $50 and a plate $5, how many of each can be bought if she takes out a loan for $6,500.
Here are the questions for this problem :
A: What do we need to find out?
B: Create the formula for this problem (Hint - Create a table using the following headings: Item, number, value, Total value. Create the unknown value and then solve)
C: Solution: How many plates at what cost?
How many tables at what cost?
How many chairs at what cost?
I got 100 plates @ $5/plate = $500
20 tables @ $100/table = $2000
80 Chairs @ $50/chair = $4000
Just need to know how to write the formula into how to solve it.
HMMMMM.
Much appreciated
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Your answers are correct.
.
Here's a way to look at it ...
.
Let x represent the number of tables. Since there are 4 chairs per table, the number of
chairs is 4x. And since there are 4 plates per table, the number of plates (not counting
20 spares) is also 4x. That means the total number of plates is 4x + 20.
.
So now we can represent the number of each quantity (tables, chairs, plates). All we have
do now is multiply each quantity by its corresponding cost and add up the total cost.
The total cost needs to be $6,500.
.
The cost of x tables at $100 per table is 100x.
.
The cost of 4x chairs at $50 per chair is 50*4x = 200x
.
The cost of 4x + 20 plates at $5 per plate is 5(4x + 20) = 20x + 100
.
The sum of all these costs is:
.
100x + 200x + 20x + 100
.
and it must equal $6500. So the equation becomes:
.
100x + 200x + 20x + 100 = 6500
.
Solve this equation by first subtracting 100 from both sides to get:
.
100x + 200x + 20x = 6400
.
Add all the terms on the left side:
.
320x = 6400
.
and solve for x by dividing both sides of this equation by 320 and the result is:
.
x = 6400/320 = 20
.
There are 20 tables, and 4 times 20 or 80 chairs, and 4 times 20 plates plus 20 spares
for a total of 80 + 20 = 100 plates.
.
And as you had figured ... 20 tables at $100 each is $2000 for tables, 80 chairs at $50
per chair is $4000 for chairs, and 100 plates at $5 each is $500 for plates. The total
is $2000 + $4000 + $500 = $6500.
.
Hope the above equation is what you were looking for.
.

RELATED QUESTIONS
Please help! I need to be able to do this type of problem for my Chemistry II class and... (answered by scott8148,jim_thompson5910)

X+9=-2 WHERE DO I START WITH THIS PROBLEM? I NEED TO KNOW ALL THE SSTEPS I USE TO SOLVE... (answered by longjonsilver)

I need help on a problem similar to this one. Show me the proper way to solve without... (answered by jim_thompson5910)

I have a problem trying to figure this out backward, can you explain this to me clearly... (answered by vertciel)

i need to how to write an answer using the following way for this problem p=(___)/____ I... (answered by josgarithmetic,MathTherapy)

2.07 x 5.3 i know the answer is 10.971 but when i do the problem on a piece of paper i... (answered by Math_prodigy)

(-1,5);m=-4/7 I have asked for help but still don't know how to get to my answer. I... (answered by Alan3354)

Ok, my algebra teacher gave us this worksheet today and he explained it, and I know what... (answered by ankor@dixie-net.com)

This was a multiple choice word problem on percents. I found the correct answer by... (answered by mananth)