Algebra ll. Number Problems

One number is 3 more than 2 times the other, and their sum is 27. Find the numbers. If x represents the smaller number, then the larger number is

2x+3

One number is 10 times as large as another, and their difference is 81. Find the numbers. If x represents the smaller number, then the larger number is

10X

One of two complementary angles is 4 degrees more than the other. Find the angles. (Recall that complementary angles are angles whose sum is 90 degrees.) Which of the following equations can not be used to solve the problem if x represents one of the angles?

2x - 4 = 90

Use the three steps to solve the problem. The sum of 3 consecutive integral numbers is 117. Find the numbers. List your answers separated by a comma.

38, 39 ,40

The length of the base of an isosceles triangle is 4 inches less than the length of one of the two equal sides of the triangles. If the perimeter is 32, find the three sides of the triangle. If x represents one of the equal sides of the triangle, then which equation can be used to solve the problem?

3x - 4 = 32

One number is 800 less than 3 times the other, and their sum is 1,200. Find the numbers. Which of the following equations can be used to solve the problem if the smaller number is x?

3x - 800 = 1,200

Use the three steps to solve the problem. The length of a rectangle is 3 times the width, and the perimeter is 22. Find the dimensions of the rectangle. Write the solution as decimals.

Width =2.75 length= 8.25

The sum of 2 consecutive numbers is 37. Find the numbers. If x represents the smaller integer, then the larger integer is

X+1

The sum of 2 consecutive odd integers is 92. Find the numbers. If x represents the smaller integer, then the larger integer is

X+2

Use the three steps to solve the problem. One number is five more than another and their sum is three less than three times the smaller. Find the numbers. List the numbers separated by a comma.

4 , 9

A man has two more nickels than dimes. He has $1.15 in all. How many coins of each kind does he have? Which equation can be used to solve the problem?

5(x + 2) + 10x = 115

One of two supplementary angles is five times the other. Find the angles. (Recall that supplementary angles are angles whose sum is 180 degrees.) Which equation can be used to solve for the smallest angle?

6X =180

Use the three steps to solve the problem. Betty has 10 more dimes than quarters. If she has $3.45, how many coins does she have?

7 quarters 17 Dimes

Use the three steps to solve the problem. Joe is 10 years older than James. In 8 years, twice Joe's age will equal three times James's age. How old is each now?

James= 12 yrs old Joe= 22 yrs old

Which of the following are steps in practical problem solving? Solve the sentence for the variable. Assign an identifying variable to the quantity to be found. Make a guess at the value of the variable. Write a sentence stating conditions placed on the quantity. Check if the value is correct.

Solve the sentence for the variable. Assign an identifying variable to the quantity to be found. Write a sentence stating conditions placed on the quantity.

Two years ago a father was four times as old as his son. Three years from now the father will be only three times as old as the son. How old is each now? If x represents the son's age two years ago, which expression represents his father's age three years from now?

X+3