Columbia theater company reviews their receipts from opening weekend. They sold 83 adult tickets and 42 child tickets on Friday night, collecting a total of $874. On Saturday night, they collected $1151 from 102 adults and 67 children. If 48 adults and 26 children attended the matinee on Sunday, how much money did the theater collect from ticket sales?

Question

16-09-2020
Mathematics

contestada

Columbia theater company reviews their receipts from opening weekend. They sold 83 adult tickets and 42 child tickets on Friday night, collecting a total of $874. On Saturday night, they collected $1151 from 102 adults and 67 children. If 48 adults and 26 children attended the matinee on Sunday, how much money did the theater collect from ticket sales?

Respuesta :

Otras preguntas

Under what circumstances may federal courts hear a case?.

A friend claims to have found the formula A= ns squared over 4 times tan theda, in a box of old math books in his grandpas attic. It appears to be a formula for

What is(are) a command(s) to see one page of a file at a time (pick two): Select one or more: a. pg b. head c. more d. ls

How would the shift in Gish populations (ie, a dedine in herring and increase in pollock in the southwest) affect the diets of the Western and Eastern ...

One problem with dynamic arrays is that they don't carry around their size. Create a structure, DynArray which uses a unique pointer for a dynamic array (data),

spencer co. has a $200 petty cash fund. at the end of the first month the accumulated receipts represent $43 for delivery expenses, $127 for merchandise invento

How much atp does oxidative phosphorylation produce?.

Simon has driven a car with a manual (stick shift) transmission all his life. After switching to an automatic, he keeps trying to step on the clutch pedal that

your customer then asks you if it would be worth the investment for them to have ethernet cabling installed to reach each of their workstations instead of conne

Which table represents only values described by the relationship between t and w? w = t + 13.3 Responses t w 2 13.5 4 13.7 6 13.9 8 14.1 t w 2 13.5 4 13.7 6 13.

MrRoyal MrRoyal · Answer 1 · 2020-09-22T02:12:45+02:00

Answer:

They made a sales for $514

Step-by-step explanation:

Represent Adult with A

Represent Children with C

Given

Friday Night: 83A + 42C = 874

Saturday Night: 102A + 67C = 1151

Required

Determine 48A + 26C

[tex]83A + 42C = 874[/tex]

[tex]102A + 67C = 1151[/tex]

Make C the subject in the first equation

[tex]83A + 42C = 874[/tex]

[tex]42C= 874 - 83A[/tex]

[tex]C = \frac{874 - 83A}{42}[/tex]

Substitute this for C in the second equation

[tex]102A + 67C = 1151[/tex]

[tex]102A + 67 * \frac{874 - 83A}{42} = 1151[/tex]

Multiply through by 42

[tex]42 * 102A + 42 * 67 * \frac{874 - 83A}{42} = 1151 * 42[/tex]

[tex]42 * 102A + 67 (874 - 83A) = 1151 * 42[/tex]

[tex]4284A + 58558 - 5561A = 48342[/tex]

Collect Like Terms

[tex]4284A - 5561A = 48342 - 58558[/tex]

[tex]-1277A = -10216[/tex]

Solve for A

[tex]A = \frac{-10216}{-1277}[/tex]

[tex]A = 8[/tex]

Recall that

[tex]C = \frac{874 - 83}{42}[/tex]

[tex]C = \frac{874 -83 * 8}{42}[/tex]

[tex]C = \frac{874 -664}{42}[/tex]

[tex]C = \frac{210}{42}[/tex]

[tex]C = 5[/tex]

Solving for 48A + 26C

[tex]48A + 26C = 48 * 8 + 26 * 5[/tex]

[tex]48A + 26C = 384 + 130[/tex]

[tex]48A + 26C = 514[/tex]

Hence, they made a sales for $514