Question

A square and a rectangle have the same perimeters. The length of a side of the square is 4x-1. The length of the rectangle is 2x+2 and the width is 2x. Write and solve an equation to find x.

A movie club charges a one-time membership fee of $25. This allows members to purchase movies for $7 each. Another club does not charge a membership fee and sells movies for $12 each. How many movies must a member purchase for the total cost of the two clubs to be equal?

How many pounds of cashews that cost $14 per pound must be mixed with 5 pounds of peanuts that cost $6.50 per pound to make mixed nuts that cost $10.25 per pound?

SHOW YOUR WORK PLEASE!

Answer 1

Answer to Ques No 1

Perimeter of the square is 4 times the side = 4*(4x-1)

Perimeter of Rectangle = 2 times length + 2 times width = 2*(2x+2) + 2*2x

Therefore,

4*(4x-1) = 2*(2x+2) +4x

16x-4= 4x+4+4x

16x-4 = 8x+4

16x-8x = 4+4

8x = 8

x = 8/8

x=1

Answer to Ques No 2

Let the number of movies be x

Total Cost at Club 1 = 25 + 7x

Total Cost at Club 2 = 12 x

Therefore,

25+7x = 12x

12x-7x=25

5x=25

x=25/5

x=5

a member must watch 4 movies for the total cost of the two clubs to be equal

Answer to Ques No 3

Let x pounds of cashews that cost $14 per pound must be mixed with 5 pounds of peanuts that cost $6.50 per pound to make mixed nuts that cost $10.25 per pound

Therefore,

14x + 5*6.50 = 10.25 (5+x)

14x + 32.50 = 52.50 + 10.25x

14x-10.25x = 52.50-32.50

3.75x = 20

x = 20/3.75

x = 5.33

5.33 pounds of cashews that cost $14 per pound must be mixed with 5 pounds of peanuts that cost $6.50 per pound to make mixed nuts that cost $10.25 per pound