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2 years ago

The largest of 2 integers is one more than three times the smaller. If the sum of the two integers is 37

Physics

1 answer:

kondor19780726 [428]2 years ago

7 0

Answer:

The two integers are 28 and 9

Explanation:

Let's call the two integers x and y.

We have:

- The largest of the 2 integers is one more than three times the smaller: this means

x = 3y + 1 (1)

- The sum of the two integers is 37:

x + y = 37 (2)

It's a system of two equations that we can solve. Substituting directly (1) into (2),

3y + 1 + y = 37

4y + 1 = 37

4y = 36

y = 9

And so,

x = 3y + 1 = 3(9) + 1 = 27 +1 = 28

So the two integers are 28 and 9.

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2 years ago

Tony drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took hours. When Tony drove hom

polet [3.4K]

Answer:

Question not completed, so I analysed the question first

Tony drove to the mountains last weekend. there was heavy traffic on the way there, and the trip took 6 hours. when tony drove home, there was no traffic and the trip only took 4 hours. if his average rate was 22 miles per hour faster on the trip home, how far away does tony live from the mountains?

Explanation:

Let use variables to solve the problems

Let the first trip to be mountain take x hours

Let the trip back home take y hours

Let the speed to while going to the mountain be a miles/hour

Then, while going home it was b miles/hour faster than while going to the mountain.

Then, speed going home is (a+b)miles / hour

The formula for speed is given as

Speed=distance/time

The constant through out the journey is distance, the two journey has the same distance.

Then,

Distance =speed×time

For first journey going to the mountain

Distance = a×x=ax miles

For the second journey going home

Distance =y×(a+b)

Distance Mountain= distance home

ax=y(a+b)

Make a subject of the formula

ax=ya+yb

ax-ya=yb

a(x-y)=yb

a=yb/(x-y)

Therefore, distance from mountain is

Distance=speed ×time

Distance= a×x=ax

Now, applying the questions

So from the questions

x=6hours, y=4hours

Also, b=22miles/hour

Then,

a=yb/(x-y)

a=4×22/(6-4)

a=88/2

a=44miles/hour

Then, the house distance from the mountain is

Distance=ax

Distance =44×6

Distance =264miles

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