Cindy took an Uber home after her night out with friends. It cost $1.79 per mile and she gave the drive a $9 tip. She spent a total of $39.43 on the trip. How many miles did Cindy travel in the Uber?
You would set up an equation to solve this problem. The variable x will represent the number of miles Cindy travels. The equations would be 39.43 = 1.79x + 9. You would start out solving the equation by subtracting 9 from both sides. Your equation will then be 30.43 = 1.79x . You would then divide each side of the equation by 1.79 and you will get 17 = x. So Cindy traveled 17 miles in the Uber.
3/5 of a pan of gooey brownies are left over from a party. You decide to eat 1/4 of the left over brownies. How much of the whole pan of brownies did you eat?
The question is looking for the amount you ate out of the total amount. You were given to parts of the whole pan of brownies so you are looking for the whole amount you ate out of the whole pan which means multiplication. It would also help to draw a picture. I drew a square and divided it up horizontally to 5 parts then shaded in 3 of those parts. I then divided the pan up vertically into 4 parts and shaded in one section. The parts that were double shaded (3) became the numerator of my answer and the total number of parts (20) in the pan was my denominator.
An exam is worth 250 points and there are 60 questions on the exam. Some of the questions on the exam are worth 3 points and some of the questions on the exam are worth 5 points. How many three point questions are on the exam? How many 5 point questions are on the exam?
You will want to set up a system of equations to solve this problem. We are going to us the variable x for number of 3 point problems and the variable y for the number of 5 point problems. The two equations are 3x + 5y = 250 and x + y = 60. The first equation is set up so we can find out how many 3 point problems are needed and how many 5 point problems are needed so the whole test will add up to 250 points. The second equation is set up because the total number of questions must add up to 60. You can solve this in many different ways. If want to convert each equation into its point slope form than graph the equations the answer is where the two lines cross. You can also solve the system of equations by the substitution method. Where you solve one equation to make it either x = or y= then plug it in to the other equation to get the first answer. You will then take that answer and plug it in to either equation to solve for the 2nd answer.