Share
The Community Relief Fund receives a large donation of $2800. The foundation agrees to spend the money on $20 school bags, $25 sweaters, $5
Question
The Community Relief Fund receives a large donation of $2800. The foundation agrees to spend the money on $20 school bags, $25 sweaters, $5 books. They want to buy 200 items and send them to schools in earthquake-hit areas. They must order as many books as school bags and sweaters combined.
in progress
0
Mathematics
4 years
2021-09-05T06:41:20+00:00
2021-09-05T06:41:20+00:00 1 Answers
75 views
0
Answers ( )
The question is incomplete:
The Community Relief Fund receives a large donation of $2800. The foundation agrees to spend the money on $20 school bags, $25 sweaters, $5 books. They want to buy 200 items and send them to schools in earthquake-hit areas. They must order as many books as school bags and sweaters combined. How many of each item should they order?
Answer:
They must order 40 bags, 60 sweaters and 100 books.
Step-by-step explanation:
From the information provided, you can write 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, you can replace (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)
Then, you will have 2 equations:
2x+2y=200 (4)
25x+30y=2800 (5)
You can isolate x in (4):
2x=200-2y
x=100-y (6)
After this, you can replace (6) in (5):
25(100-y)+30y=2800
2500-25y+30y=2800
5y=2800-2500
y=300/5
y=60
Next, you can replace the value of y in (6) to find the value of x:
x=100-60
x=40
Finally, you can replace the value of x and y in (3) to find the value of z:
z=40+60
z=100
According to this, the answer is that they must order 40 bags, 60 sweaters and 100 books.