Finding averages: Gary has averaged 5 gallons/week of gas for 1st 3 weeks of February

[HaveAQUESTION]

I managed to do most of them. But these two problems I've been stuck on for hours. I don't know what to multiply and divide by to get the answer.

(P.s. dont give me the answers , just tell me what i need to do to find them)

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7. Gary has used an average of 5 gallons of gas per week during the first three weeks of February. What is the greatest number of gallons he can use during the last week of February if he wants to decrease his average gas usage for the month by half a gallon per week?

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4. Gerard is trying to get more exercise by walking an average of two miles a day. If he walks 1.8 miles on Sunday, 3 miles on Monday, 2.4 miles on Tuesday, 1.5 miles on Wednesday, 2.2 miles on Thursday, and 1.2 miles on Friday, how many miles must he walk on Saturday to meet his average goal for the week?

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Thanks!

 

[Dr.Peterson]

I managed to do most of them. But these two problems I've been stuck on for hours. I don't know what to multiply and divide by to get the answer.

(P.s. dont give me the answers , just tell me what i need to do to find them)

---

7. Gary has used an average of 5 gallons of gas per week during the first three weeks of February. What is the greatest number of gallons he can use during the last week of February if he wants to decrease his average gas usage for the month by half a gallon per week?

---

4. Gerard is trying to get more exercise by walking an average of two miles a day. If he walks 1.8 miles on Sunday, 3 miles on Monday, 2.4 miles on Tuesday, 1.5 miles on Wednesday, 2.2 miles on Thursday, and 1.2 miles on Friday, how many miles must he walk on Saturday to meet his average goal for the week?

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Thanks!

The basic idea is to work backward. You know what the average has to be, and how many numbers are to be averaged; so what must the total be? Similarly, you know what the average has been so far, and how many numbers were averaged to get that; what is the total so far? Then, what has to be added to that to get the target total?

That's for the first (problem 7?). Problem 4 has slightly different information, but the same basic idea.

If this isn't enough, please show your own work, even if you know it's wrong; it will give us a place to start, and perhaps an error to correct.

 

[Steven G]

I managed to do most of them. But these two problems I've been stuck on for hours. I don't know what to multiply and divide by to get the answer.

(P.s. dont give me the answers , just tell me what i need to do to find them)

---

7. Gary has used an average of 5 gallons of gas per week during the first three weeks of February. What is the greatest number of gallons he can use during the last week of February if he wants to decrease his average gas usage for the month by half a gallon per week?

---

4. Gerard is trying to get more exercise by walking an average of two miles a day. If he walks 1.8 miles on Sunday, 3 miles on Monday, 2.4 miles on Tuesday, 1.5 miles on Wednesday, 2.2 miles on Thursday, and 1.2 miles on Friday, how many miles must he walk on Saturday to meet his average goal for the week?

---

Thanks!

1st problem. Gary wants the average to become 5 - 1/2 = 4 1/2.
So the number of gallons used for the 4 weeks will be 5, 5, 5 and x. x because we do not know it yet. So (5+5+5+x)/4 = 4 1/2 or 4.5. Now solve for x. In case you do not know any algebra then substitute the given choices, one by one, in for x and see if the left hand side of the equation will equal 4.5

Another way of doing this is to suppose Gary uses 5 gallons the last week. So clearly the average usage is 5 gallons per week. To reduce the average by 1/2 gallon is to realize that if we were to reduce each week by 1/2 gallons we would have used 2 gallons less. Now we can't go back for the last three weeks and reduce what we used because we already used it. So we just reduce the last week by 2 gallons.

2nd problem. Since only 14 divided by 7 equals 2, we want the sum of the 7 numbers to be 14. Work with this hint.

 

[HaveAQUESTION]

1st problem. Gary wants the average to become 5 - 1/2 = 4 1/2.
So the number of gallons used for the 4 weeks will be 5, 5, 5 and x. x because we do not know it yet. So (5+5+5+x)/4 = 4 1/2 or 4.5. Now solve for x. In case you do not know any algebra then substitute the given choices, one by one, in for x and see if the left hand side of the equation will equal 4.5

Another way of doing this is to suppose Gary uses 5 gallons the last week. So clearly the average usage is 5 gallons per week. To reduce the average by 1/2 gallon is to realize that if we were to reduce each week by 1/2 gallons we would have used 2 gallons less. Now we can't go back for the last three weeks and reduce what we used because we already used it. So we just reduce the last week by 2 gallons.

2nd problem. Since only 14 divided by 7 equals 2, we want the sum of the 7 numbers to be 14. Work with this hint.

Figure it out. Thank you.

 

[Steven G]

Figure it out. Thank you.

can you please tell us what answers you got?