Mrs. Aquino hired a caterer for her son's graduation party. $\newline$ • The caterer charges $\$135$ to cater a party for $10$ or fewer people. $\newline$ • For every $2$ additional people who attend the party, the caterer charges $\$15$ extra. $\newline$ • Mrs. Aquino spends $\$225$ on catering for the party. $\newline$ How many people are attending the party? $\newline$ $\_\_\_$ people

Full solution

Q. Mrs. Aquino hired a caterer for her son's graduation party.

\newline

• The caterer charges

\$135

to cater a party for

10

or fewer people.

\newline

• For every

2

additional people who attend the party, the caterer charges

\$15

extra.

\newline

• Mrs. Aquino spends

\$225

on catering for the party.

\newline

How many people are attending the party?

\newline

\_\_\_

people

Calculate Extra Charge: First, let's find out how much extra Mrs. Aquino paid beyond the base charge for $10$ people. $\newline$ $\$225$ (total spent) - $\$135$ (base charge) = $\$90$ (extra charge).
Determine Sets of Additional People: Now, we need to figure out how many sets of $2$ additional people this extra charge represents. $\newline$ $\$90$ (extra charge) / $\$15$ (charge per additional $2$ people) = $6$ sets of $2$ additional people.
Calculate Total Additional People: Since each set represents $2$ additional people, we multiply the number of sets by $2$ to find the total number of additional people. $\newline$ $6$ sets $\times 2$ people per set $= 12$ additional people.
Find Total Number of People: Finally, we add the additional people to the base number of $10$ people to find the total number of people attending the party. $\newline$ $10$ people (base) + $12$ people (additional) = $22$ people.