Rental cars

[huddini17]

Gambelli agency rents cars for $40 dollars per day plus 25 cents for every mile driven. Mcdougal rental rents cars for $58 per day unlimited mileage. How many miles a day can you drive a gamebelly agency car if it is cost you less than a mcdougal rental cars?

I got 58-40=18
18 X .25 = 72 miles

is this right?


How many ounces of pure water must be added to 60 oz of an 8% salt solution to make a 3% salt solution.
let's x be the pure water that should be added
I got .8(60)=4.8
4.8/60+x = 3/100
is this right so far?

 

[tkhunny]

You do seem to be doing well on your own, but you are not letting the notation help you organize or remember.

On the first, see if you can get away from your two step thought process, and get ALL the information on the page at the same time. This will help you KNOW you have the right answer.

I demonstrate:

m = miles driven

Gambelli Costs: $40 + 0.25m
McFougal Costs: $58

Then, $40 + $0.25m < $58

The result is a simple equation to be solved using standard methods.

On the second, 8% is 0.08, not 0.8

 

[soroban]

Hello, huddini17!

How many ounces of pure water must be added to 60 oz of an 8% salt solution
to make a 3% salt solution?

Since water is being added, we must think in terms of water.


The original solution is 60 oz which is 92% water.
. . It contains: .\(\displaystyle 0.92 \times 60 \,=\,55.2\text{ oz of water.}\)

We add \(\displaystyle x\) oz of water.

The mixture contains: .\(\displaystyle 55.2 + x\,\text{ oz of water.}\) .[1]


The mixture will be \(\displaystyle 60+x\) oz which is 97% water.
. . It contains: .\(\displaystyle 0.97(60+x)\,\text{ oz of water}\) .[2]


We just described the final amount of water in two ways.

There is our equation . . . . \(\displaystyle 55.2 + x \:=\:0.97(60 + x)\)

 

[tkhunny]

Note: The answer the the rental car problem is NOT "72 miles" as the problem is stated. If you get "72 miles" and someone marks it "correct", that could be a problem with understanding the meaning of words.