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Mathematics 7 Online
OpenStudy (anonymous):

The price for a gallon of super unleaded gasoline is $0.12 more than the price for a gallon of regular unleaded gasoline. Let g represent the price or regular unleaded gasoline. write an algebraic expression for the price of super unleaded gasoline @michele_Laino

OpenStudy (michele_laino):

If I call with \(s\) the price of super unleaded gasoline, and with \(r\) the price of regular unleaded gasoline, then your problem can be modeled by this equation: \(s=r+0.12\)

OpenStudy (michele_laino):

oops.. using the symbol in the text, I can write this: \(s=g+0.12\)

OpenStudy (anonymous):

thank you so much, i have one more last question

OpenStudy (michele_laino):

ok!

OpenStudy (anonymous):

how many liters of a 15% salt solution must be added to 2 liters of a 30% salt solution to yield a solution that is 18% salt

OpenStudy (michele_laino):

I call with \(x\) the requested volume in liters

OpenStudy (michele_laino):

so the total volume is \(x+2\), am I right?

OpenStudy (michele_laino):

after dilution, of course

OpenStudy (anonymous):

i got 1.82 :(

OpenStudy (michele_laino):

I'm sorry, i think that it is wrong

OpenStudy (anonymous):

i did .15x+.30(2)=.18(x+.30)

OpenStudy (michele_laino):

correct!

OpenStudy (michele_laino):

If I multiply by 100, both sides, i can write this: \(15x+60=18(x+2)\)

OpenStudy (anonymous):

so you get 15x+60=18x+2

OpenStudy (michele_laino):

please note this: I apply the distributive property of multiplication over addition at the right side, so i can write this: \(15x+60=18x+36\)

OpenStudy (michele_laino):

since: \(18 \cdot 2= 36\)

OpenStudy (anonymous):

ok?

OpenStudy (anonymous):

we subtract 15 from both sides and then will end up with 60=3x+60

OpenStudy (anonymous):

sorry we will end up with 60=3x+36

OpenStudy (michele_laino):

we subtract \(15x\) from both sides, so we have this: \(60=18x-15x+36\)

OpenStudy (anonymous):

and we will subtract the 36 from both sides to solve for x

OpenStudy (michele_laino):

yes! we get: \(60-36=18x-15x\)

OpenStudy (anonymous):

we will end up with 24=3x

OpenStudy (michele_laino):

correct!

OpenStudy (anonymous):

divide by 3 both sides will get 8

OpenStudy (anonymous):

??

OpenStudy (michele_laino):

yes! correct!

OpenStudy (anonymous):

so 8 is the answer?

OpenStudy (michele_laino):

yes!

OpenStudy (michele_laino):

\(8\) liters, of course

OpenStudy (anonymous):

thank u so much

OpenStudy (michele_laino):

:)

OpenStudy (anonymous):

story problems are soo annoying, i always have hard time solving them :(

OpenStudy (michele_laino):

no problem, here at OpenStudy we will help you! :)

OpenStudy (anonymous):

thanks :)

OpenStudy (michele_laino):

:)

OpenStudy (anonymous):

Car A and Car B enter an expressway at the same time and place, and head the same direction. Car A travels at 70 miles per hour. After 2.5 hours, car B is 50 miles behind car A. at what speed is car B traveling? I got 50mph for the final answer, is it right?

OpenStudy (michele_laino):

after 2.5 hours car A has traveled a distance of \(70 \cdot 2.5=175\) miles, and car B has traveled a distance of \(175-50 =125\) miles. So the speed of car B is: \(v=125/2.5=50\) miles/hour, so you are correct!

OpenStudy (anonymous):

good! thanks :)

OpenStudy (michele_laino):

:)

OpenStudy (anonymous):

Celine purchased a fedora. the cost o the fedora, including a 15% tax, was $ 316.25. find the cost of the fedora before tax,,, i got 268.8125 is that right?

OpenStudy (anonymous):

i multiplied .15 by 16.25= 47.4375 and then i subtract 316.25-47.4375

OpenStudy (anonymous):

i got 268.8125

OpenStudy (anonymous):

i got 268.8125

OpenStudy (anonymous):

i multiplied .15 by 16.25= 47.4375 and then i subtract 316.25-47.4375

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