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.
Im bad a these could I get some help
Sure! Let's start by assigning variables to represent the unknown quantities in the problem.
Let's use:
- Let "c" represent the number of chairs.
- Let "d" represent the number of desks.
Now, let's write two equations based on the given information.
Equation 1: The total number of chairs and desks is 14.
c + d = 14
Equation 2: The total cost of chairs and desks is $4870.
125c + 515d = 4870
Now, we have a system of two equations with two variables. We can solve this system to find the values of c and d.
To do that, we can solve Equation 1 for c, and then substitute it in Equation 2.
From Equation 1, we have: c = 14 - d
Substituting this value of c in Equation 2, we get:
125(14 - d) + 515d = 4870
Simplifying this equation gives us:
1750 - 125d + 515d = 4870
390d = 3120
d = 3120/390
d = 8
Now, substitute this value of d back into Equation 1 to find c:
c + 8 = 14
c = 14 - 8
c = 6
Therefore, the office manager bought 6 chairs and 8 desks.
In conclusion, the office manager bought 6 chairs and 8 desks.