The question appears incomplete:
The Community Relief Fund has accepted a significant donation of $2800. The foundation intends to allocate funds for $20 school bags, $25 sweaters, and $5 books. They aim to procure 200 items to send to schools in areas impacted by earthquakes. They must order the same amount of books as the total number of school bags and sweaters combined. How many of each item should they procure?
Answer:
They need to procure 40 bags, 60 sweaters, and 100 books.
Step-by-step explanation:
Based on the information given, we can derive the following equations:
x+y+z=200 (1)
20x+25y+5z=2800 (2)
z=x+y (3), where:
x=amount of bags
y=amount of sweaters
z=amount of books
Now, substituting (3) in (1) and (2):
x+y+x+y=200
2x+2y=200 (4)
20x+25y+5(x+y)=2800
20x+25y+5x+5y=2800
25x+30y=2800 (5)
We obtain 2 equations:
2x+2y=200 (4)
25x+30y=2800 (5)
We can isolate x in (4):
2x=200-2y
x=100-y (6)
Next, we can plug (6) into (5):
25(100-y)+30y=2800
2500-25y+30y=2800
5y=2800-2500
y=300/5
y=60
Now, we can substitute the value of y in (6) to find x:
x=100-60
x=40
Finally, we can replace the values of x and y in (3) to find z:
z=40+60
z=100
Thus, it is concluded that they need to order 40 bags, 60 sweaters, and 100 books.
