Question

If p = 2q² - 5 and q = 10 – 3r, find
a. p when r equals 2
b. r when p equals 67

Answer 1

When r = 2, the value of p is 27. Conversely, when p = 67, the value of r can be calculated as 4/3.

Step-by-step explanation:

Step-by-Step Solution for Finding Values of p and r

Firstly, we are given that p = 2q² - 5 and q = 10 – 3r. To find p when r equals 2, we replace r with 2 in the equation for q to find q, and then use that q to find p.

1. Calculate q: q = 10 - 3(2) q = 10 - 6 q = 4
2. Using q, calculate p: p = 2(4)² - 5 p = 2(16) - 5 p = 32 - 5 p = 27 So, when r = 2, p = 27.

To find r when p equals 67, we set up the equation p = 2q² - 5 and solve it for q first, then use the q to find r.

1. Solve for q: p = 67 67 = 2q² - 5 72 = 2q² q² = 36 q = ±6 (Taking the positive value since q = 10 - 3r, and q must be positive as r is subtracted from 10)
2. Using q, calculate r: 6 = 10 - 3r 3r = 10 - 6 3r = 4 r = 4/3 So, when p = 67, r = 4/3.

The solutions are p = 27 when r = 2 and r = 4/3 when p = 67.