Kelsey is knitting baby items to sell at a craft fair. she has a total of 1,620 yards of yarn to use for the items. a pair of mittens uses 81 yards of yarn and a blanket uses 162 yards. she wants to knit a minimum of 12 items for the fair. if the solution region represents the number of pairs of mittens and blankets that kelsey can knit, determine which graph represents the solution set to the system of inequalities representing this situation.

With some give information, we need to solve some algebraic problems that involve a change of units, lets see step by step how we do that:

A) First, we know that:

The bridge was constructed in 2.5 years

Knowing that 1 year =  12 months, we can rewrite:

2.5 years = (2.5)*(12 montsh) = 28 months

The two crews built, together, 12,513 ft of the bridge.

Now, we know that the South Padre Island crew built an average of 208.5 per month.

Then in the 28 months for the whole construction, they built 28 times that amount:

D = (28 months)*(208.5 per month)  = 5,838 ft

Then the rest was constructed by the Port Isabel Crew.

They constructed 12,513 ft -  5,838 ft = 6,675ft

So that crew constructed 6,675 ft in 28 months, then the average number of feet built per month (the quotient between the total amount built and the number of months in which that was built) is:

6,675 ft/28 months = 238.39 ft per month.

b)

South Padre Island crew constructed  5,838 ft

Port Isabel Crew constructed 6,675ft

Now we want to transform these to miles.

Remember that;

1 mille = 5280 ft.

Then to transform from ft to miles, we just need to divide our measures by 5280 ft

Then:

South Padre Island crew constructed  5,838 ft = (5,838ft/5280ft) mi = 1.11 mi

Port Isabel Crew constructed 6,675ft = (6,675ft/5280ft) mi = 1.26 mi

c) Is this answer reasonable?

Mathematically, yes, both crews constructed about the same in about the same time, with a small difference that may be related to the sizes of each crew or something like that.

We could conclude that this would not be reasonable if the monthly rates were dramatically different.

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