Question

The value of (a × n + b) is 242 when (n = 40). What are the possible values for (a) and (b)? Show your work to demonstrate that the value for (a × (n + b)) equals 242.

a) (a = 6, b = 202)
b) (a = 4, b = 82)
c) (a = 5, b = 192)
d) (a = 3, b = 122)

Answer 1

To find the possible values of a and b, we substitute n = 40 into the given equation and simplify. The possible values for a and b are (a = 6, b = 202), (a = 4, b = 82), (a = 5, b = 192), and (a = 3, b = 122).

Step-by-step explanation:

To find the values of a and b, we can use the given equation (a × n + b) = 242 when n = 40. Substitute n = 40 into the equation:

(a × 40 + b) = 242

Simplify the equation:

40 × a + b = 242

We can rewrite this equation as:

b = 242 - 40 × a

Now, we can substitute different values of a and solve for b. Using the given options:

a) For (a = 6), b = 242 - 40 × 6 = 202

b) For (a = 4), b = 242 - 40 × 4 = 82

c) For (a = 5), b = 242 - 40 × 5 = 192

d) For (a = 3), b = 242 - 40 × 3 = 122

Therefore, the possible values for (a) and (b) are:

a) (a = 6, b = 202)

b) (a = 4, b = 82)

c) (a = 5, b = 192)

d) (a = 3, b = 122)