My brain hurts from to much math help please word problem?

Question

Snookers lumber can convert logs into lumber or plywood. In a given day the mill turns out twice as many units of plywood as limber. It makes a profit of $25 on a unit of lumber and $45 on a unit of plywood. How many of each unit must be produced and sold in order to make a profit of $11960?

Units of Lumber -----

Units of plywood -----

Answer 1

let x be the number of lumber the mill produces and sells in a given day

therefore the number of plywood the mill will be producing and selling in a given day is twice the number of lumber, which will be: 2x

regardless of the amount of units sold, the profit on each type will be:

lumber:  $25x

plywood:  $45(2x)

and the sum of this must give a total profit of $11960

this will be used to form the equation:

25x + 45(2x) = 11960

solving, we have

25x + 90x = 11960

therefore x = 11960 / 115 = 104

LUMBER (x)  produced and sold will be 104 units

PLYWOOD (2x) produced and sold will be: 104 * 2 = 208 units

hope this helps!!!!

Answer 2

Sometimes word problems can be a little overwhelming. Lets look at this problem in the simplest way possible. We know that the relationship between plywood and lumber is that  

2 * lumber = plywood.

Now lets use p  to equal the number of plywood units made. Then lumber = 0.5p

Since the profit on plywood is 45, we get that the total profit for plywood is  45p, or the cost of plywood times the the total number of plywood units sold. Using the same logic, we get that the total profit for the lumber units sold is 25(0.5p).

Now we put these into the equation to equal the total profit and solve for p.

45p + 25(0.5p) = 11960

45p + 12.5p = 11960

57.5p = 11960

p = 11960 / 57.5 = 208 units

Since the total number or lumber units sold is 0.5p, we get that the number of lumber units sold is

lumber = 0.5 * 208 = 104 units

Hence, using the chart, we get

units of lumber = 104

units of plywood = 208

Answer 3

Hi,

Let x = # of units of lumber

Then 2x = # of units of plywood

25x + 45(2x) = 11960

25x + 90x = 11960

115x = 11960

x = 104 units of lumber <==ANSWER

2x = 208 units of plywood <==ANSWER

I hope that helps!! :-)

Answer 4

Let L represent the units of lumber produced and sold, and P represent the units of plywood produced and sold.

Since it says the mill turns out twice as much plywood as lumber, we have the equation

P = 2L

Then since each unit of lumber gives a profit of $25 and each unit of plywood gives a profit of $45, and we want to make $11960, we form the equation

25L + 45P = 11960

Then plugging the relation P = 2L into this equation, we have

25L + 45(2L) = 11960

25L + 90L = 11960

115L = 11960

L = 104

Then since P = 2L, we have P = 2(104) = 208.

So,

Units of lumber: 104

Units of plywood: 208