Question

a football game a vendor sold a combined total of 134 sodas and hot dogs The number of sodas sold was 58 more than the number of hot dogs sold Find the number of sodas and the number of hot dogs sold

Answer 1

96 sodas

38 hot dogs

Step-by-step explanation

Step 1

Set the equations:

let x represents the number of sodas sold

let y represents the number of hot dogs sold

then

a)a football game a vendor sold a combined total of 134 sodas and hot dogs

rewrite

`x+y=134\Rightarrow equation(1)`

b)The number of sodas sold was 58 more than the number of hot dogs sold( in other words, you have to add 58 to the number of hot dogs sold to get the number of sodas sold)

so

`x=y+58\Rightarrow equation(2)`

Step 2

Solve the equations

a)replace the x value from equation (2) into equation(1)

`\begin{gathered} x+y=134\Rightarrow equation(1) \\ (y+58)+y=134 \\ \text{add like terms} \\ 2y+58=134 \\ \text{subtract 58 in both sides} \\ 2y+58-58=134-58 \\ 2y=76 \\ \text{divde both sides by 2} \\ (2y)/(2)=(76)/(2) \\ y=38 \end{gathered}`

hence

the number of hot dogs sold is 38

B)now, replace the y value into equation(1) and so

`\begin{gathered} x+y=134\Rightarrow equation(1) \\ \text{replace} \\ x+38=134 \\ \text{subtract 38 in both sides} \\ x+38-38=134-38 \\ x=96 \end{gathered}`

therefore

the number of sodas sold is 96

I hope this helps you

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