Question

A soccer match was held between Peru and Bolivia with 38,000 in attendance. Adult tickets sold for $8 and children's tickets sold for $5. Total sales were $257.125.How many adults and children were attendance? Define the variables. Write and solve a system of equations.

Answer 1

The System of equations are
`\left \{ {{x+y =38,000} \atop {8x+5y=257,125}} \right.`

There were 22375 adults and 15625 children attended the soccer match.

Explanation:

Given,

Total number of people attending the soccer match = 38000

Let the number of adults be 'x'.

Let the number of Children be 'y'.

So Total number of people attending the soccer match is equal to sum of the number of adults and the number of Children.

framing in equation form we get;

`x+y =38000 \ \ \ \ \ equation \ 1`

Also Given:

Cost of Adult ticket = $8

Cost of Children ticket = $5

Total Sales = $257,125

So we can say that Total Sales is equal to the number of adults multiplied by Cost of Adult ticket and the number of Children multiplied by Cost of Children ticket.

framing in equation form we get;

`8x+5y=257,125 \ \ \ \ \ equation \ 2`

So The System of equations are
`\left \{ {{x+y =38,000} \atop {8x+5y=257,125}} \right.`

On Solving the above system of equation we get

Now Multiplying equation 1 with 5 we get;

`5(x+y)= 38000*5\\\\5x+5y= 190000 \ \ \ \ equation \ 3`

Now Subtracting equation 3 from equation 2 we get;

`(8x+5y)-(5x+5y)=257,125-190000\\\\8x+5y-5x-5y=67125\\\\3x=67125\\\\x=(67125)/(3) = 22375`

Now Substituting the value of x in equation 1 we get;

`x+y=38000\\\\22375+y =38000\\\\y=38000-22375 = 15625`

Hence There were 22375 adults and 15625 children attended the soccer match.