Each hotdog cost $1.50 and sodas cost $.50. At the end of the day you made a total of $78.50. You sold a total of 87 hot dogs and sodas combined. How many hotdogs and sodas were sold?

35 hotdogs and 52 sodas were sold.

Step-by-step explanation:

Create equations to represent the problem.

let "d" be the number of hotdogs sold

let "a" be the number of sodas sold

1.5d + 0.5a = 78.50 Equation for money made

d + a = 87 Equation for items sold

Rearrange d + a = 87 to isolate one of the variables.

a = 87 - d

Substitute a for 87-d into the other equation. Isolate using reverse operations.

1.5d + 0.5a = 78.50

1.5d + 0.5 (87 - d) = 78.50 Distribute over brackets by multiplying

1.5d + 43.5 - 0.5d = 78.50 Collect like terms

43.5 + d = 78.50 1.5d - 0.5d is 1d. You don't need to write "1".

43.5 + d - 43.5 = 78.50 - 43.5 Isolate d, subtract 43.5 from both sides

d = 35 Number of hotdogs sold

Substitute d for 35 in the simpler equation

d + a = 87

35 + a = 87 Subtract 35 form both sides to isolate "a".

a = 87 - 35

a = 52 Number of sodas sold

Therefore 35 hotdogs and 52 sodas were sold.