System of Equations - Word Problems online exercise for | Live ... - Free Printable

Explanation:
Let’s solve each problem one by one.

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Problem 1:
Kristin spent $131 on shirts. Fancy shirts cost $28 each, plain shirts cost $15 each. She bought 7 shirts total. How many of each kind?

Let:
- $ f $ = number of fancy shirts
- $ p $ = number of plain shirts

We know:
1) $ f + p = 7 $ (total shirts)
2) $ 28f + 15p = 131 $ (total cost)

From (1): $ p = 7 - f $

Substitute into (2):
$ 28f + 15(7 - f) = 131 $
$ 28f + 105 - 15f = 131 $
$ (28 - 15)f + 105 = 131 $
$ 13f + 105 = 131 $
$ 13f = 131 - 105 = 26 $
$ f = 26 ÷ 13 = 2 $

Then $ p = 7 - 2 = 5 $

✔ Check: 2 fancy × $28 = $56; 5 plain × $15 = $75; $56 + $75 = $131 ✔️

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Problem 2:
13 animals total: chickens and pigs. Chickens have 2 legs, pigs have 4 legs. Total legs = 40.

Let:
- $ c $ = number of chickens
- $ g $ = number of pigs (using *g* for pig to avoid confusion with *p* for plain shirt earlier — but it's fine; just be clear)

Equations:
1) $ c + g = 13 $
2) $ 2c + 4g = 40 $

Simplify (2) by dividing by 2:
$ c + 2g = 20 $

Now subtract (1) from this:
$ (c + 2g) - (c + g) = 20 - 13 $
$ g = 7 $

Then $ c = 13 - 7 = 6 $

✔ Check: 6 chickens × 2 = 12 legs; 7 pigs × 4 = 28 legs; 12 + 28 = 40 ✔️

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Problem 3:
10 animals: pigs and ducks. Pigs have 4 legs, ducks have 2 legs. Total legs = 36.

Let:
- $ p $ = pigs
- $ d $ = ducks

Equations:
1) $ p + d = 10 $
2) $ 4p + 2d = 36 $

Simplify (2) by dividing by 2:
$ 2p + d = 18 $

Now subtract (1) from this:
$ (2p + d) - (p + d) = 18 - 10 $
$ p = 8 $

Then $ d = 10 - 8 = 2 $

✔ Check: 8 pigs × 4 = 32 legs; 2 ducks × 2 = 4 legs; 32 + 4 = 36 ✔️

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Problem 4:
195 students went on a trip. They used 7 vehicles: some cars (5 students each), some buses (45 students each). Find how many cars and how many buses.

Let:
- $ c $ = number of cars
- $ b $ = number of buses

Equations:
1) $ c + b = 7 $
2) $ 5c + 45b = 195 $

Simplify (2) by dividing by 5:
$ c + 9b = 39 $

Now subtract (1) from this:
$ (c + 9b) - (c + b) = 39 - 7 $
$ 8b = 32 $
$ b = 4 $

Then $ c = 7 - 4 = 3 $

✔ Check: 3 cars × 5 = 15 students; 4 buses × 45 = 180 students; 15 + 180 = 195 ✔️

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Final Answer:
1) 2 fancy shirts, 5 plain shirts
2) 6 chickens, 7 pigs
3) 8 pigs, 2 ducks
4) 3 cars, 4 buses