# Tutor profile: Darren O.

## Questions

### Subject: Pre-Algebra

Simplify: (4*4)^2 + 4*4^2

First, simplify within parentheses = (4*4) = 16^2 + 4*4^2 Second, simpligy exponents = 256 + 4*16 Third, multiply = 256 + 64 Finally, add = 320

### Subject: Basic Math

A box weighs 54.4 lbs and contains 150 bolts. If the container itself weighs 2 lbs, how much does each bolt weigh?

First, find the weight of the bolts by subtracting the weight of the container: 54.4 lbs - 2 lbs = 52.4 lbs Then, divide this amount by the total number of bolts to find the weight of each bolt: 52.4 lbs/150 = 0.349 lbs per bolt.

### Subject: Algebra

The perimeter of a rectangular lost is 400 ft. The length of the lot is 10 ft more than twice the width. Find the dimensions of the lot.

The formula for perimeter is 2L + 2W = P, where L represents the length, W represents the width, and P represents the perimeter. Recall that our perimeter is 400 ft. Therefore, our equation is 2L + 2W = 400. The length is 20 ft more than twice the width. "More than" equates to addition and "twice" represents multiplication by 2. L can be written as L = 2W + 20. Using substitution, our equation now looks like 2(2W+20) + 2W = 400. We now solve for W. First distribute: 2*2W+2*20 + 2W = 400 4W+40 + 2W = 400 Combine like terms: 4W+2W + 40 = 400 6W + 40 = 400 6W + 40 - 40 = 400 - 40 6W = 360 6W/6 = 360/6 W = 60 Now substitute 60 for W in L = 2W + 20. L = 2(60) + 20 L = 120 + 20 L = 140 The width of the rectangle is 60 ft and its length is 140 ft.

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