Question

monday nights homework
problems 1 - 4: a copy machine can make 500 copies every 4 minutes.

1. how many copies can the copy machine make per minute?
2. how many minutes does it take per copy?
3. how many copies can the copy machine make in 10 minutes?
4. a teacher made 700 copies. how long did it take?

problems 5 - 7: jamars class painted 50 square feet of a mural using 4 cans of paint.

1. how many square feet did they paint per can of paint?
2. how many cans did they use per square foot?
3. jamars class wants to paint a total of 310 square feet. jamar calculated that they would need 3,875 cans of paint. here is his work.

is jamar correct? circle one. then explain your thinking.
yes no
jamar
12.5 square feet
310 · 12.5 = 3875
problems 8 - 9: evaluate each expression.

1. \\( \frac { 1 } { 4 } \\) of 60
2. \\( \frac { 3 } { 4 } \\) of 60

Explanation:

Step1: Calculate copies per minute

Given 500 copies every 4 minutes. To find copies per minute, divide total copies by total minutes. So, \( \frac{500}{4}=125\) copies per minute.

Step2: Calculate time per copy

Since 125 copies are made in 1 minute. Time per copy is \( \frac{1}{125}=0.008\) minutes per copy.

Step3: Calculate copies in 10 minutes

If 125 copies are made in 1 minute. In 10 minutes, copies \(=125\times10 = 1250\) copies.

Step4: Calculate time for 700 copies

Since 125 copies are made in 1 minute. Time for 700 copies \(=\frac{700}{125}=5.6\) minutes.

Step5: Calculate square feet per can

Given 50 square feet with 4 cans. Square feet per can \(=\frac{50}{4} = 12.5\) square feet per can.

Step6: Calculate cans per square foot

Cans per square foot \(=\frac{4}{50}=0.08\) cans per square foot.

Step7: Check Jamar's calculation

If 1 can paints 12.5 square feet. For 310 square feet, cans needed \(=\frac{310}{12.5}=24.8\) cans. Jamar calculated \(310\times12.5 = 3875\) which is wrong.

Step8: Calculate \(\frac{1}{4}\) of 60

\(\frac{1}{4}\times60 = 15\)

Step9: Calculate \(\frac{3}{4}\) of 60

\(\frac{3}{4}\times60=45\)

Answer:

1. 125
2. 0.008
3. 1250
4. 5.6
5. 12.5
6. 0.08
7. No
8. 15
9. 45