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nikdorinn [45]
2 years ago
14

The ratio of the amount of money Karen had to the amount of money Peter had was 2 : 5. After Peter received $75 from his mother,

the ratio of the amount of money Karen had to the amount of money Peter had became 4 : 15. How much money did each person have at first?
Mathematics
1 answer:
Viefleur [7K]2 years ago
4 0

Answer:

$60 and $150

Step-by-step explanation:

Initially

Karen : Peter = 2 : 5

After Peter receiving $75 the ratio is

4 : 15

We can suppose that initally the amount of monye Karen has is 2x and Peter is 5x.

The new ratio is

2x :  (5x +75)  = 4 :15

2x (15)= 4 (5x +75)

30 x = 20 x + 300

10 x = 300

x = 30

So at first Karen has 2x =60 dollars while Peter has 5x = 5(3) = 150 dollars.

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The quantity of each type of seats sold are as follows:

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According to the question,there are four times as many 3D, x seats as Dinner and a Movie, y seats.

That is, x = 4y

Also, total seats

= (x) + (y) + (z) = 3000...….............eqn(1)

Also, If the theater brings in $53,000 when tickets to all 3000 seats are sold.

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By substituting 4y for x in equations 1 and 2; we have;

<em>5y + z = 3000</em>..…........eqn(3) and

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By solving equations 3 and 4 simultaneously; we have;

y = 200 and z = 2000

and since x = 4y

x = 800

The quantity of each type of seats sold is as follows:

  • Standard viewing = 2000

  • 3D seats = 800

  • Movie and a dinner seat = 200

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brainly.com/question/12413726

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