Algebra 2 Word Problems

Question

1) Find two consecutive odd integers who product is 143.

 

2) What is the length of the side of a square if its area and perimeter are numerically equal?

 

3) A projectile is fired straight up from the ground level. After t seconds its height, s, in feet above the ground, is given by: s = 220t - 16t^2

At what times is the projectile exactly 750 feet above the ground?

Answer 1

1)

 

The consecutive odd integers are n and n + 2.

 

n(n + 2) = 143

 

n² + 2n - 143 = 0 

 

Note we can factor the quadratic equation above.

 

(n + 13)(n - 11) = 0

 

This gives two values of n:  n = -13, 11

 

So there are two pairs of consecutive odd integers that when multiplied give 143:

 

(i)   -13 and -11

(ii)  11 and 13 

 

2)

A = L²
P = 4L

If numerically equal (ignoring units), then

A = P ⇒ L² = 4L

L = 4

 

3)

 

s = 220t - 16t²

 

750 = 220t - 16t²

 

Divide through by 2 to simplify a little:

 

375 = 110t - 8t²

 

8t² - 110t + 375 = 0

 

t = [1/(2*8)] {110 ± √[(110)² - 4(8)(375)]} = (1/16) (110 ± 10) = 6.25 or 7.5 seconds

 

There are two times:

 

At t₁ = 6.25 s, it reaches 750 ft on the way up, and at t₂ = 7.5 seconds, it reaches 750 ft again on the way down.