1. A newspaper charges $50 per half-page ad and $80 per full-page ad. Gavin has a budget of $750 to purchase 12 advertisements.

(a) Define a variable for each unknown. Write a system of equations to represent the situation.

(b) How many half-page advertisements does Gavin purchase? Show your work.

(c) How many full-page advertisements does Gavin purchase? Show your work.

5 full page ads, 7 half page ads

Step-by-step explanation:

a) Let's say Gavin buys x half page ads and y full page ads

sum of ads = x + y = 12

total amount charged for half page ads = 50 per half page ad = 50 for each x = 50 * x

total amount charged for full page ads = 80 * y

total amount charged for all ads = 50x + 80y = 750

here is our system of equations:

x + y = 12

50x + 80y = 750

b and c)

solve for x in the first equation by subtracting y from both sides

x = 12 - y

plug this into the second equation to make it so that there is only one variable

50(12-y) + 80y = 750

600 - 50y + 80y = 750

600 + 30y = 750

subtract 600 from both sides to isolate y and its coefficient

30y = 150

divide both sides by 30 to isolate y

y = 5

he buys 5 full page ads and 12-y = 12-5 = 7 half page ads

step-by-step explanation: