Question

As junior employee in your office, you are sent out to get hamburgers and hot dogs for the 23 people who work there. On the way, you forget how many of each to buy. So you decide to figure it out by algebra. Each person gets one burger or one dog (not both!). You have collected a total of $32.10. Burgers cost $1.50 each and dogs cost $1.10 each. How many of each should you buy?

Answer 1

Let x be the number of hamburger and y be the number of hot dogs

x + y = 23 -----------------------------------(1)

1.50x + 1.10y = 32.10 -------------------------------(2)

We can now solve this simultaneosly

Multiply through equation (1) by 1.50

1.50x + 1.5y = 34.5 ----------------------------(3)

1.50x + 1.10y = 32.10 --------------------------(4)

subtract equation (4) from (3)

0.4y = 2.4

Divide both-side of the equation by 0.4

y = 6

substitute y=6 into equation (1) and then solve for x

x + 6 = 23

subtract 6 from both-side of the equation

x = 23 - 6

x= 17

The number of hamburgers are 17

The number of hot dogs are 6