# Thread: algebra inequality help

1. ## algebra inequality help

Jabari is training for a marathon and is using a Pyramid training pattern for the next five days. He plans to increase the number of miles he runs by a single mile each day from the first to the third day, peaking on the third day, and then decreasing the number of miles run by a single mile per day for the last two days.

a) If x represents the number of miles Jabari runs on Day 1, write expressions for how many miles, in terms of x, he runs for Days 2 through 5.

Day 1 = x Day 2 = Day 3 = Day 4 = Day 5 =

b) Find all possible values that Jabari can run on Day 1 such that his total number of miles run over the five days is at least 55. Represent your answer algebraically

3) Assuming Jabari runs a whole number of miles on Day 1, what is the least number of miles he can run on Day 1 to meet his goal of at least 55 miles.

2. Originally Posted by sri340 Jabari is training for a marathon and is using a Pyramid training pattern for the next five days. He plans to increase the number of miles he runs by a single mile each day from the first to the third day, peaking on the third day, and then decreasing the number of miles run by a single mile per day for the last two days.

a) If x represents the number of miles Jabari runs on Day 1, write expressions for how many miles, in terms of x, he runs for Days 2 through 5.

Day 1 = x Day 2 = Day 3 = Day 4 = Day 5 =

b) Find all possible values that Jabari can run on Day 1 such that his total number of miles run over the five days is at least 55. Represent your answer algebraically

3) Assuming Jabari runs a whole number of miles on Day 1, what is the least number of miles he can run on Day 1 to meet his goal of at least 55 miles.

Hi sri340,

a) It would seem to me that

Day 1 = x
Day 2 = x + 1
Day 3 = x + 2
Day 4 = x + 1
Day 5 = x

(b) And in order to insure he runs at least 55 miles total,

x + x+1 + x+2 + x+1 + x >= 55

This boils down to x >= 10.2 miles for day 1.

(c) If he runs a whole number of miles on day 1, and still maintains at least 55 miles over the 5 days, he would have to run 11 miles on day 1, 12 on day 2, 13 on day 3, 12 on day 4, and 11 on day 5 making a total of 59 miles.

### jabri is training for a marathon and is using a pyramid training patternfor the next five days

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