A surf shop rents surfboards and charges x dollars for one rental day. it gives a discount for a weekly seven day rental and only charges 5x. On a Saturday shop rents 20 boards for a one day rental and 10 boards at the weekly rate and had total sales of $600.

A. How much did the shop charge to rent a board for a one-day rental?

B. How much does the shop charge for a weekly rental?

A. The shop charges $8.517 for a one-day rental

B. The shop charges $42.857 for a weekly rental.

Step-by-step explanation:

Step 1; The shop charges $x for a one-day rental and $5x for a weekly rental. Assume $x = a and $5x = b, from this we can write,

5a = b, take this as equation 1.

Step 2; The shop had a total sale of $600 by renting 20 boards for a one-day rental and 10 boards for a weekly rental. So,

20a + 10b = 600, take this as equation 2.

Substituting equation 1 in 2, we get

20a + 10 (5a) = 600,

20a + 50a = 600, a = 600 / 70,

a = $8.5714.

From equation 1, 5a = b,

5 * $8.5714 = b,

b = $42.857.

So for a one-day rental, the shop charges $8.5714 and for a weekly rental it charges $42.857.