Question

1.Write this sentence as an equation.Do not solve it.

Two times the difference of three times a number and seven is a number.

7.B'Elanna Torres tries to combine her like terms in 3(2x+4)-2x and got out 16x but Tom Paris thinks she made a mistake.It is your job to explain her mistake and solve the problem correctly.
Mistake: 3(2x+4)-2x=16x

3.The YMCA has a new rectangular pool with a perimeter of 108ft.The deep ends length is d ft.The shallow ends length is 15 ft.MacGyver knows that the width of the entire pool is 3 ft less than the deep ends length and can be represented by d-3.Solve for d.​

Answer 1

Problem 1

x = some unknown number

3x = three times a number

3x-7 = difference of three times a number and seven

2(3x-7) = two times the difference of three times a number and seven

2(3x-7) = x

The last equation is formed because the expression we built up is equal to the original number in question

Answer: 2(3x-7) = x

===========================================================

Problem 2

Use the distribution rule to get

3(2x+4)-2x

3*2x+3*4-2x

6x+12-2x

From here, we combine like terms. That means we combine the 6x and -2x to get 4x

So 6x+12-2x simplifies to 4x+12 and not 16x

How did she get 16x? Possibly because she mistakenly thought she could add 4x to 12 to get 16x. This only works if the 12 had x attached to it.

In other words, this is valid: 4x+12x = 16x but this is not 4x+12 = 16x

===========================================================

Problem 3

L = length = horizontal dimension = (d+15) ft

W = width = vertical dimension = (d-3) ft

P = perimeter of the rectangle = 108 ft

P = 2(L+W)

108 = 2(d+15+d-3)

108 = 2(2d+12)

108 = 4d+24

4d+24 = 108

4d = 108-24

4d = 84

d = 84/4

d = 21

The deep end is 21 feet long.

This means the overall horizontal length is d+15 = 21+15 = 36 feet and the the vertical width is d-3 = 21-3 = 18 feet

The overall dimensions of the rectangular pool are 36 ft by 18 ft

Answer: d = 21