|
Question 446315: I'm having a hard time putting this word problem into an algebraic equation, can some one help?
If you have $10 and gas is $3.99 a gallon, how many gallons of gas can you buy and how much if anything is left over to buy a soda for $1.69?
Like usual when I'm trying to change words in equations I always end up with 2 equal signs which I know can't be right.
Thanx
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! I'm going to assume that the question is looking for you to buy whole gallons. In other words, you are not to assume that you could buy 2.3 gallons or some similar amount.
That being said, I'm going to introduce you to the mathematical concept of integer notation. Integer notation is indicated by two vertical bars. If a number is between these two vertical bars, you are to consider only the whole number (or integer) portion between the bars. For example |36.17| ... the answer is 36 ... only the whole number part. Another example, |14.995| ... the answer is 14, the whole number part.
That being said, how many whole gallons of gas can you buy if gas is $3.99 per gallon and you have $10. Simple, enough ... just divide $10 by $3.99 per gallon and you get an answer of 2.506 gallons. But you are only going to buy whole gallons. Therefore, you are going to buy 2 gallons and you will have some money left over because 2 gallons of gas at $3.99 per gallon costs you 2 times $3.99 or a total of $7.98. That means you will have $2.02 left over ($10 minus $7.98) and you can afford to get a $1.69 drink.
You can write this in the form of a mathematical statement as follows:
Let A equal the amount of money you have for gas.
Let P equal the price per gallon
Let D equal the cost of a drink
We start with A. Then, just as we did above, we divide A by P, take the integer part of that answer, multiply that integer part times P (the price per gallon). Then we subtract the price we pay for whole gallons from $10. We look at that amount left over and subtract the cost of a drink from it. If the answer is + (positive) or 0, you have enough to buy a drink. (If drinks were cheaper, you might even be able to afford more than 1.)
As a mathematical statement we could write the method as:
A - |A/P|*P - D
and look to see if the answer is + or zero.
For this problem, we substitute the values into the mathematical statement of the method as follows:
10 - |10/3.99|*3.99 - 1.69
We already know that |10/3.99| is |2.506| and the integer part is 2
Substituting into the math statement we get:
10 - 2*3.99 - 1.69
Multiplying the middle term to get 2*3.00 = 7.98
10 - 7.98 - 1.69
Combining the first two terms results in 10 - 7.98 = 2.02 and we substitute that for the first two terms to get:
2.02 - 1.69 = +0.33
The answer is positive meaning you can afford a drink and still have 33 cents left over from the $10 you started with after you pay for the gas and one drink.
Hope that this line of thinking helps you to understand the problem a little better.
|
|
|
| |
