Question

P is 6 times Q, and Q is 2 less than 9 times R. Which of the following statements describes the relationship between P and R ?

1) P is 2 less than 15 times R.
2) P is 2 less than 54 times R.
3) P is 12 less than 15 times R.
4) P is 12 less than 54 times R.
5) P is 18 less than 15 times R.

Answer 1

The relationship between P and R is found by first expressing Q as 9R - 2 and then expressing P as 6 times Q, resulting in the equation P = 54R - 12. Thus, P is 12 less than 54 times R.

Step-by-step explanation:

The relationship between P and R is derived from the given statements: 'P is 6 times Q, and Q is 2 less than 9 times R.' To express P in terms of R, we follow these steps:

1. Write the relationship of Q to R: Q = 9R - 2.
2. Substitute the value of Q into the expression for P: P = 6 * (9R - 2).
3. Expand the equation: P = 54R - 12.

This gives us the expression for P in terms of R, which is 'P is 12 less than 54 times R.'

Hence, the correct statement describing the relationship between P and R is: P is 12 less than 54 times R. This corresponds to option 4.