karen received some gift cards for music and movie downloads for her birthday. Using one of them, she downloaded eight songs and

Question

3 years ago

13

karen received some gift cards for music and movie downloads for her birthday. Using one of them, she downloaded eight songs and

nine movies, which cost a total of $115. Using another, she purchased 15 songs and nine movies, which cost a total of $129. How much does each download cost?

Mathematics

1 answer:

finlep [7] · Answer 1 · 2022-07-02T19:15:00+03:00

One song download costs $2 and one movie download costs $11.

Step-by-step explanation:

Let,

Price of one song download = x

Price of one movie download = y

According to given statement;

8x+9y=115 Eqn 1

15x+9y=129 Eqn 2

Subtracting Eqn 1 from Eqn 2

$(15x+9y)-(8x+9y)=129-115\\15x+9y-8x-9y=14\\7x=14$

Dividing both sides by 7

$\frac{7x}{7}=\frac{14}{7}\\x=2$

Putting x=2 in Eqn 1

$8(2)+9y=115\\16+9y=115\\9y=115-16\\9y=99$

Dividing both sides by 9

$\frac{9y}{9}=\frac{99}{9}\\y=11$

One song download costs $2 and one movie download costs $11.

Keywords: linear equation, elimination method

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