A radio station is raising money for charity. Listeners can pledge $10 to dedicate a song or $25 to wish someone Happy Birthday. Forty-two listeners made one pledge each and the station collected $630. Write and solve a system of equations to find the number of songs that were dedicated and the number of birthday wishes.

Question

21-11-2022
Mathematics

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A radio station is raising money for charity. Listeners can pledge $10 to dedicate a song or $25 to wish someone Happy Birthday. Forty-two listeners made one pledge each and the station collected $630. Write and solve a system of equations to find the number of songs that were dedicated and the number of birthday wishes.

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tutorconsortium123 tutorconsortium123 · Answer 1 · 2022-11-23T05:35:27-05:00

Solve a system of equations we get 28 number of songs that were dedicated and 14 number of birthday wishes.

What is a system of equations ?

system of equations, or simultaneous equations Two or more equations to be solved concurrently in algebra (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns.

Let x be No.of Listeners dedicate a song

y be the No. of Birth day wishes.

$10 to dedicate a song or $25 to wish someone Happy Birthday.

Forty-two listeners made one pledge each .

X+Y =42.

y = 42 -x

the station collected $630.

10x + 25y = 630

y = 42 -x in above equation .

10x + 25(42 -x) = 630

10x -25x +1050 = 630

-15x = 630 -1050 = -420

x = 420/15

x = 28

y= 14

we get 28 number of songs that were dedicated and 14 number of birthday wishes.

To learn more about system of equations refer,

https://brainly.com/question/25869125

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tutorconsortium127 tutorconsortium127 · Answer 2 · 2022-11-24T10:59:03-05:00