Ms. Green and Mr. White took their science classes to the museum. Ms. Green spent $262$ $\$$ to buy $28$ student tickets and $4$ adult tickets for her class. Mr. White spent $191$ $\$$ for $22$ student tickets and $2$ adult tickets for his class. $\newline$ How much did the student tickets for both classes cost in total? $\newline$ $\$$ $\_\_\_$

Full solution

Q. Ms. Green and Mr. White took their science classes to the museum. Ms. Green spent

262

\$

to buy

28

student tickets and

4

adult tickets for her class. Mr. White spent

191

\$

for

22

student tickets and

2

adult tickets for his class.

\newline

How much did the student tickets for both classes cost in total?

\newline

\$

\_\_\_

Set up equations: Step $1$ : Set up equations for each teacher's expenses. $\newline$ Ms. Green: $262 = 28s + 4a$ $\newline$ Mr. White: $191 = 22s + 2a$ $\newline$ Here, ' $s$ ' represents the cost of one student ticket, and ' $a$ ' represents the cost of one adult ticket.
Solve for 'a': Step $2$ : Solve for 'a' using the equations. $\newline$ Multiply Mr. White's equation by $2$ to align the coefficients of 'a': $\newline$ $2(191) = 2(22s + 2a)$ $\newline$ $382 = 44s + 4a$ $\newline$ Now subtract Mr. White's modified equation from Ms. Green's equation: $\newline$ $262 - 382 = (28s + 4a) - (44s + 4a)$ $\newline$ $-120 = -16s$ $\newline$ $s = 7.5$
Substitute and calculate: Step $3$ : Substitute the value of $s$ back into Mr. White's original equation to find $a$ . $191 = 22(7.5) + 2a$ $191 = 165 + 2a$ $26 = 2a$ $a = 13$
Calculate total cost: Step $4$ : Calculate the total cost of student tickets for both classes. $\newline$ Total student tickets cost = $(28 + 22) \times 7.5$ $\newline$ Total student tickets cost = $50 \times 7.5$ $\newline$ Total student tickets cost = $375$