Question

question 1-5
lee is packing a truck with small and large filing cabinets. the large cabinets weigh 40 pounds, and the small cabinets weigh 25 pounds. to optimize the load, the total load weight should be 1850 pounds from a total of 65 cabinets. how many of each size of cabinet should lee pack in the truck?
small cabinets
large cabinets

Explanation:

Step1: Define variables

Let \( x \) be the number of small cabinets and \( y \) be the number of large cabinets. We have two equations:

1. \( x + y = 65 \) (total number of cabinets)
2. \( 25x + 40y = 1850 \) (total weight in pounds)

Step2: Solve the first equation for \( x \)

From \( x + y = 65 \), we get \( x = 65 - y \).

Step3: Substitute \( x \) into the second equation

Substitute \( x = 65 - y \) into \( 25x + 40y = 1850 \):
\[
25(65 - y) + 40y = 1850
\]
\[
1625 - 25y + 40y = 1850
\]
\[
1625 + 15y = 1850
\]

Step4: Solve for \( y \)

Subtract 1625 from both sides:
\[
15y = 1850 - 1625
\]
\[
15y = 225
\]
Divide both sides by 15:
\[
y = \frac{225}{15} = 15
\]

Step5: Solve for \( x \)

Substitute \( y = 15 \) into \( x = 65 - y \):
\[
x = 65 - 15 = 50
\]

Answer:

Small cabinets: 50, Large cabinets: 15