snookers lumber can convert logs into either lumber of plywood. in a given day, the mill turns out three times as many units of plywood as lumber. it makes a profit of $20 on a unit of lumber and $50 on a unit of plywood. how many of each unit must be produced and sold in order to make a profit of $17170?

Question

snookers lumber can convert logs into either lumber of plywood. in a given day, the mill turns out three times as many units of plywood as lumber. it makes a profit of $20 on a unit of lumber and $50 on a unit of plywood. how many of each unit must be produced and sold in order to make a profit of $17170?

snookers lumber must produce and sell ?
___ units of lumber

and

___ units of plywood to make a profit of $17170

Answer 1

"... the mill turns out three times as many units of plywood as lumber"

If L stands for the units of lumber, then 3L is the number of units of plywood.

"it makes a profit of $20 on a unit of lumber and $50 on a unit of plywood"

$20*L is the profit on lumber, and
$50*(3L) is the profit on plywood.

Total profit = $17170 = $20*L + $50*(3L)
Solve for L.

Answer 2

To find the number of units of lumber and plywood that Snookers Lumber needs to produce and sell in order to make a profit of $17,170, we need to set up a system of equations.

Let's assume that the number of units of lumber produced is x, and the number of units of plywood produced is y.

Given that the mill turns out three times as many units of plywood as lumber, we can write the equation:

y = 3x

Next, we can calculate the profit made on each unit of lumber and plywood:

Profit per unit of lumber = $20
Profit per unit of plywood = $50

Now, we can set up the equation for the total profit:

Total profit = (Profit per unit of lumber * Number of units of lumber) + (Profit per unit of plywood * Number of units of plywood)

Substituting the values, we have:

$17,170 = ($20 * x) + ($50 * y)

We can substitute the value of y from the previous equation into the equation for total profit:

$17,170 = ($20 * x) + ($50 * 3x)

Simplifying the equation:

$17,170 = $20x + $150x
$17,170 = $170x

Now, we can solve for x:

x = $17,170 / $170
x ≈ 101

Therefore, Snookers Lumber needs to produce and sell approximately 101 units of lumber.

To find the number of units of plywood, we can substitute the value of x into the equation for y:

y = 3 * x
y = 3 * 101
y ≈ 303

Therefore, Snookers Lumber needs to produce and sell approximately 303 units of plywood.

In conclusion, Snookers Lumber needs to produce and sell:

101 units of lumber
and
303 units of plywood to make a profit of $17,170.

"... the mill turns out three times as many units of plywood as lumber"

See also:

To find the number of units of lumber and plywood that Snookers Lumber needs to produce and sell in order to make a profit of $17,170, we need to set up a system of equations.