Vincent works in a factory of eyeglasses. He's paid 20 pesos per eyeglass for the first 10 eyeglasses, 50 pesos for the next 10 eyeglasses, and 75 for each set of 10 eyeglasses in excess of 20. Write a piecewise function G(x) that represents Vincent's earnings.
To write the piecewise function, we need to consider the different ranges of values of x.
1. For the first 10 eyeglasses, Vincent is paid 20 pesos per eyeglass. So for 0 ≤ x ≤ 10, his earnings can be calculated as:
G(x) = 20 * x
2. For the next 10 eyeglasses (11 ≤ x ≤ 20), Vincent is paid 50 pesos per eyeglass. So his earnings for this range can be calculated as:
G(x) = 20 * 10 + 50 * (x - 10) = 200 + 50 * (x - 10)
3. For each set of 10 eyeglasses in excess of 20 (x > 20), Vincent is paid 75 pesos per eyeglass. So his earnings for this range can be calculated as:
G(x) = 20 * 10 + 50 * 10 + 75 * (x - 20) = 700 + 75 * (x - 20)
Putting it all together, the piecewise function that represents Vincent's earnings, G(x), is:
G(x) =
20 * x if 0 ≤ x ≤ 10
200 + 50 * (x - 10) if 11 ≤ x ≤ 20
700 + 75 * (x - 20) if x > 20
just write what they told you, using math.
G(x) =
{20x for x ≤ 10
{200+50x for 10 < x ≤ 20
{700+75x for x > 20