A GROUP OF FRIENDS WENT OUT TO LUNCH. EACH BROUGHT A HAMBURGER AND A SOFT DRINK. TOGETHER A HAMBURGER AND A SOFT DRINK COST MORE THAN A DOLLAR. THE TOTAL COST FOR THE GROUP WAS $17.81. THERE WAS NO TAX OR TIP INCLUDED.
IF A HAMBUGER COSTS 2 CENT MORE THAN TWICE A SODA, FIND THE COST OF THE HAMBURGER.
Word problems such as these require that we first translate them into math symbols. If we read the problem through, we see that what we need to find out is the cost of the hamburger but the hamburger's price is defined in terms of the price of the soft drink. So let's define our unknowns as follows:
Let s = the cost of the soft drink Then h = 2s + 2 = the cost of the hamburger (2 cents more than twice a soft drink)
We have one more unknown to deal with and that is the number of people who ate.
Let n = the number of people who ate. Note that this value must be a whole number.
Now we can go ahead and make an equation to solve.
We know that n people each had a hamburger and a soft drink and that the total bill came to $17.81. Let's deal in cents only so we have no decimal places.
n(2s + 2 + s) = 1781 or in simplified form: n(3s + 2) = 1781
Now we also know that the cost of a hamburger and a soft drink together cost more than one dollar so s must be greater than or equal to 33.
Lets make a table to sort the information. Choosing different values for s, lets see if we get whole numbers for n when we substitute into the equation.
Notice that 1781 is an odd number. In order to get n as a whole number, the expression (3s+2) must also be odd. If (3s+2) is odd, then our s value must also be odd. So we don't even have to check even values for s.
s = 33 ==> n is approximately 17.63 -- not a whole number so s is not 33 cents
s = 35 ==> n is approximately 16.64 -- not a whole number so s is not 35 cents
s = 37 ==> n is approximately 15.76 so s is not 37 cents
If you keep checking odd values for s, you will eventually find one that results in a whole number value for n. Using that s value you can then calculate the cost of the hamburger.
Hope this helps,