George wants to buy pets for each of his 5 grandchildren if he buys 3 pooples and 2 cats he will spend 1200 if he buys 2 poodles and 3 cats he will spend 1050. find the cost of a poodle and cat

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George wants to buy pets for each of his 5 grandchildren if he buys 3 pooples and 2 cats he will spend 1200 if he buys 2 poodles and 3 cats he will spend 1050. find the cost of a poodle and cat

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marcthemathtutor marcthemathtutor · Answer 1 · 2025-03-22T23:20:57-04:00

Answer:

Each poodle = $300

Each Cat = $150

Step-by-step explanation:

Let number of poodles be P and number of cats be C

"if he buys 3 pooples and 2 cats he will spend 1200" mathematically:

3P + 2C = 1200-------eq 1

"2 poodles and 3 cats he will spend 1050" mathematically:

2P + 3C = 1050 ------eq 2

So now we have a system of 2 equations with 2 unknowns, we'll solve by elimination

eq 1 x 3 : 3 (3P + 2C) = 3 (1200)

9P + 6C = 3600 ------ eq 3

eq 2 x 2: 2(2P + 3C) = 2(1050)

4P + 6C = 2100---------eq 4

By elimination : eq 3 - eq 4

(9P + 6C) - (4P + 6C) = 3600 - 2100

9P - 4P = 1500

5P = 1500

P = 300 (answer)

Substituting back into eq 1

3(300) + 2C = 1200

900 + 2C = 1200

2C = 1200 - 900

2C = 300

C = 150(answer)