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Nimfa-mama [501]
3 years ago
12

There were 80 runners to start a race. In the first half of the race, 1/4 of them dropped out. In the second half of the race, 2

/5 of the remaining runners dropped out. How many runners finished the race?
Mathematics
1 answer:
IgorLugansk [536]3 years ago
7 0

Answer:

36 runners finished the race.

Step-by-step explanation:

In the first half of the race, 1/4 of them dropped, so we need to calculate 1/4 of 80:

(1/4) * 80 = 80/4 = 20

If 20 runners dropped out, now we have 80 - 20 = 60 runners.

Then, in the second half, 2/5 of the remaining runners dropped out, so:

(2/5) * 60 = 2*60/5 = 120/5 = 24

If 24 runners dropped out, now we have 60 - 24 = 36 runners.

So, 36 runners finished the race.

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Answer:

The system of equations is:

x + y = 42

4x + 2y = 120

And there are 24 chickens.

Step-by-step explanation:

We know that the total number of cows (x) plus the total number of chickens (y) is 42, because Farmer Brown has 42 animals.

We also know that cows (x) have 4 legs and so 4 times the number of cows is the number of cow legs. And chickens (y) have 2 legs, so the number of chickens times two represents the total chicken legs. The sum of 4x + 2y is 120 because there are 120 legs in total.

To solve the system of equations, first solve each equation for y.

In the first equation:

x + y = 42

Subtract x from both sides to isolate y.

y = 42 - x

Second equation:

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Subtract 4x from both sides

2y = 120 - 4x

Divide both sides by 2

y = 60 - 2x

Now that the y's are isolated in both equation, you can put them into 1 equation. Where y = y:

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Subtract 42 from both sides

x = 18

Since x is the number of cows, we know that Farmer Brown has 18 cows.

Now we can substitute the x value into one of the equations:

y = 42 - x

y = 42 - (18)

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