Algebra 1 question

Question

At a baseball game, a vender sold a combined total of 231

sodas and hot dogs. The number of sodas sold was two times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.

Answer 1

1) Define your variables

s = number of sodas sold

h = number of hot dogs sold

2) Write a system of equations

s + h = 231 [total number of items sold]

s = 2h [number of sodas sold was twice the number of hot dogs sold]

3) Substitute the value of s from the second equation into the first equation

s + h = 231

2h + h = 231

4) Solve for h

2h + h = 231

3h = 231

h = 77 hot dogs sold

5) Plug in the value of h into one of the original equations

s = 2(77) = 154 sodas sold

6) Check your work by plugging the values of h and s into the other equation

s + h = 231

154 + 77 = 231

231 = 231 ✓

Answer: 154 sodas and 77 hot dogs were sold.

Answer 2

H = no. hot dogs S = no. sodas

We know that the total sold is 231, so H + S = 231

Also, sold twice as many sodas as hot dogs, so S = 2H

Can substitute to eliminate one of the variables: H + 2H = 231 -> 3H = 231

Divide both sides by H: H = 231/3 = 77 hot dogs.

Then S = 231 - H or 231 - 77 = 154 sodas (154 is 2 x 77, so it checks).