I'm studying and I'm stuck with this problem. As this isn't an algebra class, I can't remember any algebra to solve it. I know the answer is really obvious, I just can't seem to make my brain remember.
The price of gasoline is represented by y=0.72445+0.0306x, with x being the price of crude oil. How much would the price of crude have to increase to yield a 20-cent increase in the price of gas?
I'm not so much looking for the answer as I'm looking for HOW to solve it. Thanks for your help.
The price of gasoline is represented by y=0.72445+0.0306x, with x being the price of crude oil. How much would the price of crude have to increase to yield a 20-cent increase in the price of gas?
I'm not so much looking for the answer as I'm looking for HOW to solve it. Thanks for your help.
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A simple trick to use when solving problems of this type is to ITERATE: that is, assign a nominal value for y, and solve for x. For example, let y be $1.00 per gallon (I wish!). Solve for y to find out what x is now:
y = 0.72445 + 0.0306x
1.00 = 0.72445 + 0.0306x <-----now subtract 0.72445 from each side
0.27555 = 0.0306x <-----now divide both sides by 0.0306
9.005 = x
Now you know that a value of $9.005 for crude oil gives you a price of $1.00 for gas. But that's not what we want to know - we want to know how much x increases if the price goes up to $1.20. Let's use the same equation, but put in $1.20 for y:
y = 0.72445 + 0.0306x
1.20 = 0.72445 + 0.0306x <-----again, subtract 0.72445 from both sides
0.47555 = 0.0306x <-----now divide by 0.0306 again
15.541 = x
Now you know the amount of x that gives you a result of $1.20 per gallon. But this STILL isn't the number we want - we want how much x had to INCREASE to get us an increase of $0.20 in the price. We know that by subtracting the former value for x from the current:
INCREASE = $15.541 - $9.005 = $6.54 <-----and THAT'S the answer!
y = 0.72445 + 0.0306x
1.00 = 0.72445 + 0.0306x <-----now subtract 0.72445 from each side
0.27555 = 0.0306x <-----now divide both sides by 0.0306
9.005 = x
Now you know that a value of $9.005 for crude oil gives you a price of $1.00 for gas. But that's not what we want to know - we want to know how much x increases if the price goes up to $1.20. Let's use the same equation, but put in $1.20 for y:
y = 0.72445 + 0.0306x
1.20 = 0.72445 + 0.0306x <-----again, subtract 0.72445 from both sides
0.47555 = 0.0306x <-----now divide by 0.0306 again
15.541 = x
Now you know the amount of x that gives you a result of $1.20 per gallon. But this STILL isn't the number we want - we want how much x had to INCREASE to get us an increase of $0.20 in the price. We know that by subtracting the former value for x from the current:
INCREASE = $15.541 - $9.005 = $6.54 <-----and THAT'S the answer!