Solving Linear Equation Word Problems Algebraically
Solve each word problem using an algebraic solution in one variable.
1) The sum of four consecutive integers is 194. Find the integers.
2) Seven less than four times a numbers is 13. What is the number?
3) Find two consecutive odd integers whose sum is 128.
4) Two thirds of a number decreased by 12 is equal to four more than the number. Find the number.
5) The length of a rectangle is 3 more than its width. If the perimeter is 38 inches, then find the
dimensions of the rectangle.
6) Find three consecutive even integers such that the sum of the first integer and three times the last
integer is 20 less than 5 times the second integer.
7) Two angles are complementary. The measure of one angle is 5 less than four times the measure of
the other angle. Find the number of degrees in the measure of the larger angle.
8) Four times the sum of a number and 5 is -16. Find the number.
9) The perimeter of a square, whose adjacent sides are represented by 3x and 2x + 3, is equal to the
perimeter of an equilateral triangle whose side is represented by 5x – 3. Find the value of x.
10) The tickets sold for a dance recital cost $5 for adults and $2 for children. If the total number of
tickets sold was 295 and the total amount collected was $1,220, how many tickets were sold to adults
and to children?
11) Jim keeps quarters, nickels, and dimes in his change jar. He has three more quarters than dimes and
five fewer nickels than dimes. If there are 52 coins in the change jar, how many of each coin are in the
jar?
12) Tickets sales for a music concert totaled $2160. Three times as many tickets were sold for the
Saturday night concert as were sold for the Sunday afternoon concert. Two times as many tickets were
sold for the Friday night concert as were sold for the Sunday afternoon concert. Tickets for all three
concerts sold for $2 each. Find the number of tickets sold for the Saturday night concert.
13) In triangle ABC, the measure of angle B is 21 less than four times the measure of angle A, and the
measure of angle C is 1 more than five times the measure of angle A. Find the measure of each angle.
14) Twice the sum of a number and 9 is the same as four times the difference obtained when 6 is
subtracted from the number. What is the number?
15) Find four consecutive integers whose sum is 15 less than 5 times the first.