Lupe and her friends spend $20 on hot dogs and popcorn at a sporting event. Hot dogs cost $2.50 each, and popcorn costs $1.00
each. They buy a total of 11 items at the concession stand. How
many of each item do they buy?

They buy 6 hotdogs and 5 popcorn

Step-by-step explanation:

Assume that they buy x hotdogs and y popcorn

∵ They buy a total of 11 hotdogs and popcorn

∵ The number of hotdogs is x and the number of popcorn is y

∴ x + y = 11 ⇒ (1)

∵ Hot dogs cost $2.50 each

∵ Popcorn costs $1.00 each

∵ They spend $20 on hot dogs and popcorn

→ Multiply x by 2.5 and y by 1, add the products and equate the sum by 20

∴ 2.5(x) + 1(y) = 20

∴ 2.5x + y = 20 ⇒ (2)

Now we have a system of equations to solve it

→ Subtract equation (1) from equation (2)

∵ (2.5x - x) + (y - y) = (20 - 11)

∴ 1.5x + 0 = 9

∴ 1.5x = 9

→ Divide both sides by 1.5 to find x

∴ x = 6

→ Substitute the value of x in equation (1) to find y

∵ 6 + y = 11

→ Subtract 6 from both sides

∴ 6 - 6 + y = 11 - 6

∴ y = 5

∴ They buy 6 hotdogs and 5 popcorn

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