The length of a rectangle is five times its width. The perimeter of the rectangle is at most 96 cm.
Which inequality models the relationship between the width and the perimeter of the rectangle?
L = 5W
Perimeter = 2 [ W + L ]
So......substituting for the width, we have
2 [ W + 5W ] ≤ 96 simplify
2 [ 6W ] ≤ 96
12W ≤ 96
Reiko started a business selling home medical supplies. She spent $6500 to obtain her merchandise, and it costs her $550 per week for general expenses. She earns $900 per week in sales.
What is the minimum number of weeks it will take for Reiko to make a profit?
We actually just need to equate costs and sales....so we have....
6500 + 550W = 900W where W is the number of weeks that we are trying to find
Subtract 550W from both sides
6500 = 350W
Divide both sides by 350
18.57 ≈ W .....so...it will take her 19 weeks to start making a profit
Ron is five years older than twice his cousin Pat’s age. The sum of their ages is less than 35.
What is the greatest age that Pat could be?
Let Pat's age = P
Ron's age = 2P + 5
And we know that
P + (2P + 5) < 35 simplify
3P + 5 < 35 subtract 5 from both sides
3P < 30 divide both sides by 3
P < 10 → Pat's greatest possible age is 9