I do not have to solve the problem--I need to make an equation or two that would HELP me be able to solve it.
Tommy's Lumber can convert logs into either lumber or plywood. In a given day, the mill turns out twice as many units of plywood as lumber. It makes a profit of $25 on a unit of lumber and $40 on a unit of plywood. How many units of each type must be produced and sold in order to make a profit of $10,920?
My teacher said I would probably need to make 2 equations, each with 2 variables. I do not know how to take the information to make an equation? Can anyone help me make 2 equations with this info?
Thanks so much!
let the number of units of lumber be x
let the number of units of plywood be y
your first equation is y = 2x or
2x - y = 0
form the second equation just like you did for the other questions.
I would not use two variables here.
the part where it says, "the mill turns out twice as many units of plywood as lumber" tells me to define
pieces of lumber --- x
pieces of plywood -- 2x
then 25x + 40(2x) = 10920
etc
To solve the problem, we need to define the variables and set up equations based on the given information.
Let's assume:
L = the number of units of lumber produced and sold in a given day
P = the number of units of plywood produced and sold in a given day
Based on the given information, we can establish two equations:
1. The mill turns out twice as many units of plywood as lumber:
P = 2L
2. The profit from the sales of lumber and plywood is $25 and $40 per unit, respectively, and the total profit required is $10,920:
25L + 40P = 10,920
By substituting equation 1 into equation 2, we can replace P with 2L:
25L + 40(2L) = 10,920
25L + 80L = 10,920
105L = 10,920
Now, solve for L by dividing both sides of the equation by 105:
L = 10,920 / 105
Calculate L using a calculator or long division:
L ≈ 104.19
Since you cannot have a fraction of a unit, round L to the nearest whole number:
L ≈ 104
Substitute this value back into equation 1 to find P:
P = 2(104)
P = 208
So, to make a profit of $10,920, Tommy's Lumber needs to produce and sell approximately 104 units of lumber and 208 units of plywood.