joe and mo sold drinks and hot dogs. drinks were $3 and hit dogs were $4. They sold a total of 84 items and made a total of $285. How many drinks and how many hot dogs did they sell?

Answer 1

Let d = the number of drinks sold

Let h = the number of hot dogs sold

the total number of items sold = the number of drinks sold + the number of hot dogs sold = d + h = 84

The total amount of money made equals the money made selling drinks plus the money made selling hot dogs = $285

The money made selling drinks = the cost of a drink times the number of drinks sold = $3d

The money made selling hot dogs = the cost of a hot dog times the number of hot dogs sold = $4h

The total amount of money made = $3d + $4h = $285

This gives us 2 equations and two unknowns

d + h = 84

and

3d + 4h = 285

Solving by substitution:

1. Solve the first equation for d or h

d + h = 84

d = 84 - h

1. Substitute into the second equation

3d + 4h = 285

3(84 - h) + 4h = 285

1. Solve for one variable.

3(84) - 3h + 4h = 285

252 + h = 285

h = 285 -252 = 33

1. Substitute the solution back into the first equation to solve for the 2nd variable

d + h = 84

d + 33 = 84

d = 84-33 = 51

1. Check your answer by substituting the solution into the 2nd equation

3d + 4h = 285

3(51) + 4(33) = 153 + 132 = 285

1. Answer the question

They sold 51 drinks and 33 hot dogs.

Answer 2

Use x to represent the number of drinks sold and use y to represent the number of hot dogs sold.

Then x+y=84 and 3x+4y=285.

Now subtract y from both sides of the first equation to get x=84-y.

Then substitute this into the second equation to get 3(84-y)+4y=285.

Distribute and combine like terms to get 252-3y+4y=y+252=285.

Subtract 252 from both sides to get y=33.

Substitute back into the first equation to get x+33=84.

Subtract 33 from both sides to get x=51.

So Joe and Mo sold 51 drinks and 33 hot dogs.

You can check your work by multiplying 51⋅$3=$153, and 33⋅$4=$132, then adding $153+$132=$285.

Answer 3

3D + 4H = 285

D+H = 84

3D + 3H = 252

subtract that last equation from the 1st to eliminate D and solve for H

H = 33 hot dogs sold

D = 84 -33 = 51 drinks sold

33(4) + 51(3) = 132 + 153 = 285