Question

Coach Tassone had to buy new equipment for the football team. He bought 15 new items He bought jerseys, which were $38 cach, and helmets, which were $S6 each, and paid a total of $678.00. How many jerseys did he buy and how many helmels did he buy? Solve using the eliniination methed

Answer 1

we can write an equation from each statement

Coach Tassone had to buy new equipment for the football team. He bought 15 new items

we add the number of each item and the total is 15

so

`j+h=15`

where j is the number of jerseys and h the number of helments

He bought jerseys, which were $38 cach, and helmets, which were $S6 each, and paid a total of $678.00

we multiply the number of each item by the price and add all to obtain the total cost

`38j+56h=678`

so, we have two equations and two unknowns

`\begin{gathered} j+h=15 \\ 38j+56h=678 \end{gathered}`

We use the elimination method

multiply the first equation by -38

`\begin{gathered} j(-38)+h(-38)=15(-38) \\ -38j-38h=-570 \end{gathered}`

now we add the equations

`\begin{gathered} -38j-38h=-570\text{ +} \\ 38j+56h=678 \\ ------------------ \\ 0j+18h=108 \end{gathered}`

now we can solve for h

`\begin{gathered} 18h=108 \\ h=(108)/(18) \\ \\ h=6 \end{gathered}`

the number of helmets is 6, now we can repalce the value of h on any equation to find j

i will replace on the first equation

`\begin{gathered} j+h=15 \\ j+6=15 \\ \end{gathered}`

solve for j

`\begin{gathered} j=15-6 \\ j=9 \end{gathered}`

the number of jerseys is 9