Question

1. Lilly has two cousins. One of the cousins is 7 years older than Lilly. The other cousin is 3 years younger than Lilly. The product of Lilly’s cousins' ages is 24. How old is Lilly?

2. Jackie is building a rectangular football field that has an area of 6000 square yards. The football field must be 40 yards longer than its width. Determine the width of the football field, in yards.

3. James is reading a book and noticed the page numbers are consecutive integers whose product is 1640. What is the value of the larger page number?

Answer 1

Answer: a. 5 years

b. 60 yards

c. 41

Explanation:

1. Let Lily's age be x.

One of the cousins is 7 years older than Lilly. The age will be = x + 7

The other cousin is 3 years younger than Lilly. The age will be = x - 3

Therefore, (x + 7)(x - 3) = 24

x² - 3x + 7x - 21 = 24

x² + 4x - 21 - 24 = 0

x² + 4x - 45 = 0

x² + 9x - 5x - 45 = 0

(x² + 9x) - (5x - 45) = 0

x(x + 9) - 5(x + 9) = 0

(x - 5)(x + 9) = 0

(x - 5) = 0

x = 0 + 5

x = 5

Therefore, Lily is 5 years

2. Let the width be represented by x

Therefore, length will be x + 40.

Area = length × width

6000 = x(x + 40)

x² + 40x = 6000

x² + 40x - 6000 = 0

x² + 100x - 60x - 6000 = 0

x(x + 100) - 60(x + 100) = 0

(x - 60)(x + 100) = 0

x - 60 = 0

x = 0 + 60 = 60

Therefore, the width is 60 yards

3. Let the consecutive numbers be x and x+1.

Therefore, x(x + 1) = 1640

x² + x = 1640

x² + x - 1640 = 0

x² + 41x - 40x - 1640 = 0

x(x + 41) - 40(x + 41) = 0

(x - 40) = 0

x = 0 + 40

x = 40

Larger number = x + 1 = 40 + 1 = 41