The money collected from a Saturday car wash are directly proportional to the number of cars washed. The total money collected after 7 cars is $140. Write an direct variation equation relating the money collected (m) and the number of cars washed

Step-by-step explanation:

Let m represent the total money collected and c represent the amount of cars washed.

We know that the money collected is directly proportional to the number of cars washed. So, we can write the following equation:

Where k is a constant.

We know that the money collected after 7 car washes is $140. So, let's find our k by substituting 140 for m and 7 for c. This yields:

Find k. Divide both sides by 7:

So, the value of k is 20.

We can now substitute k back into our direct variation equation:

This means that every car costs $20 to wash.

And we're done!

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!