An office manager spent $4870 on a total of 14 chairs and desks. Each chair costs $125, and each desk costs $515. How many chairs and how many desks did he buy? Create and solve a system of equations to solve the problem(Identify what your variables represent). Write a sentence stating the solution.

Question

An office manager spent $4870 on a total of 14 chairs and desks. Each chair costs $125, and each desk costs $515. How many chairs and how many desks did he buy? Create and solve a system of equations to solve the problem(Identify what your variables represent). Write a sentence stating the solution.

help pls

Answer 1

IN OTHER WORDS, R_scott,

d = 14 - c
515*(14 - c) + 125c = 4870
7210 - 515c + 125c = 4870
(125 - 515)c = 4870 - 7210
(515 - 125)c = 7210 - 4870
390c = 2340
c = 6
d = 14 - c = 14 - 6 = 8
Double-checking, we get
c + d = 6 + 8 = 14.
It passed test 1. Test 2:
125*6 + 515*8 = 750 + 4120 = 4870.
It passed the second test.
That's six chairs and eight desks, though god knows what psycho would buy more desks than chairs. *shudder*

Answer 2

d + c = 14 ... 125 d + 125 c = 1750

515 d + 125 c = 4870

subtract the equations to eliminate c
... solve for d
... substitute back to find c

Answer 3

dear Anonymous,

I know you mean well ; but the idea of setting up the solution
... so that the questioner can solve it , gives them some "hands on"
... work to familiarize themselves with the process
... we call it "learning"

Answer 4

To solve this problem using a system of equations, we need to identify the two unknown variables. Let's denote the number of chairs as 'c' and the number of desks as 'd'.

The total number of chairs and desks is given as 14, so we can write our first equation:
c + d = 14 ...(Equation 1)

The total amount spent, $4870, can be expressed by multiplying the cost of each chair by the number of chairs and the cost of each desk by the number of desks:
125c + 515d = 4870 ...(Equation 2)

Now we have a system of equations to solve. We can use substitution or elimination method to find the values of 'c' and 'd'.

Let's solve this system:

From Equation 1, we can rewrite it as c = 14 - d.

Substituting this expression for 'c' into Equation 2:
125(14 - d) + 515d = 4870

Simplifying the equation:
1750 - 125d + 515d = 4870
390d = 3120
d = 8

Now that we know d = 8, we can substitute it back into Equation 1 to find the value of 'c':
c + 8 = 14
c = 14 - 8
c = 6

Therefore, the office manager bought 6 chairs and 8 desks.

The solution is: The office manager bought 6 chairs and 8 desks.