Math Word Problems

Question

1. A student scores of 84 and 92 on the first two tests in her Algebra 2 class. What score does she need to get on the third test to make an average on the three tests 90 so that she can get an 'A' in the course?
2. A rectangle is twice as long as it is wide and has a perimeter of 300 feet. What is the area of the rectangle?
3. A man is 3 times as older than his daughter. The sum of their ages is 48. How old is his daughter?
4. A coin purse contains nickels, dimes, and quarters worth $2.05. There are twice as many quarters as nickels and one more dime than quarter. How many coins of each type are in the purse?
5. A married couple takes their three children to a ball game. A ticket for a child costs 40% less than a ticket for an adult. If the admission for the family is $130, what is the cost of a ticket for an adult?

Answer 1

First problem

There are 3 tests; let the anticipated coming grade be x.

Then the average of 3 scores is

(84 + 92 + x)/3 = 90 in order to get "A'.

Now solve the equation for x: (176 + x)/3 = 90

176 + x = 270

x = 94

You can check the answer. The sum of all three grades 84 + 92 + 94 = 270. You can find average by dividing 270 by 3 and will get 90! So the answer is correct. Answer: 94

Problem two

Let x be the width of the rectangle. Then its length is 2x.

The perimeter of the rectangle is 2(x + 2x) or 6x and is equal to 300.

Now we have simple equation

6x = 300

Which gives us x = 50.

It means that the width of the rectangle is 50 ft and its length 100 ft.

To find the area we need multiply width by length: 50 x 100 = 5 000

Answer: 5,000 square feet

Problem three

Let the age of the daughter be x. Then the age of the man, who is three times older, is 3x.

We know that the sum of their ages is 48. Hence we can write the equation:

x + 3x = 48 or 4x = 48

Solving for x, we will get that x = 48/ 4 or x = 12

Answer: the daughter is 12

years old

Now try to use the same approach to do the rest of the problems. Good luck!