Algebraic Expressions
Four more than the price, p
p + 4
Solve:
m ?+ 2.3 = 9.4
m=7.1
Write an equation:
The sum of fifteen and six times a number t is eighty-one. What is the number?
6t ?+ 15 = 81
Solve.
2m + 7 = 9
1
Adding integers with same sign
? ?? -36 + -17
-53
25 − 0.6x
Sample answer: $25 minus six-tenths of x
Solve:
z ?+ 2.3 = 0.46
z=2.76
Write an equation:
An electrician charges $40 to come to your house. She also charges $55 for each hour that she works. The electrician charges you a total of $190. How many hours does the electrician work at your house? Use h for the number of hours
40 ?+ 55h = 190
Rewrite each equation so it is in the form ax + b = c then solve
3x − 17 = x + 3
2x ?- 17=3; x =10
Adding integers with different signs
-12 + 5
7
Write an algebraic equation:
Twenty customers bought the portable drill when it was on sale. Twelve of the customers also bought the charger that goes with it.
20d + 12c,
Solve:
A painter works 37.5 hours one week. If she worked 5 days, how many hours did she work on average per day?
5h=37.5, h=7.5
Write an equation:
A taxi charges $1.75 plus a fee of $0.75 for each mile traveled. The total cost of a ride, without a tip, is $4.75. How many miles is the trip? Use m for the number of miles traveled.
1.75 ?+ 0.75m = 4.75
Explain how to solve the two-step equation. Then solve it.
15 − 4t = 3
Subtract 15 from both sides; ?-4t = ?- 12. Then divide both sides by ?-4; t = 3.
Estimate the answers:
The average mass of the eggs laid by chickens on Ms. Watson’s farm is 3.5 grams. About how many grams does a dozen eggs weigh?
Answers may vary. Sample answer: 3-gram eggs would be 36 grams, but 4 gram eggs would be 48 grams, so a dozen 3.5-gram eggs should be about 42 grams.
Write an algebraic equation
Thirty percent of the green house flowers are added to 25 ferns for the school garden.
0.3f ?+ 25
Solve:
Fifteen tickets cost $193.75. What is the average cost of each ticket?
15t= 193.75; t= $12.92 (to the nearest cent)
Write a two-step equation to represent each problem:
Twelve and three tenths more than five and thirteen thousandths of a number d is equal to fifteen and three hundred two thousandths. What is the value of d?
12.3 ?+ 5.013d = 15.302
Write an equation to represent the problem. Then solve:
When 3 is subtracted from two times a number, the result is 17. What is the number?
2n − 3 = 17; n = 10
Find the percent increase:
From 42 acres to 72 acres
71%
Solve:
A construction worker bought several bottles of juice for $3 at the convenience store. She paid for them with a $20 bill. If j represents the number of bottles of juice, write an expression for the change she should receive.
20 ?- 3j
Solve:
Eric had 15.3 feet of fishing line. He cut off a piece and had 38.4 inches left. How long was the piece he cut?
38.4 in=3.2 ft; 15.3 ?- x = 3.2, x =12.1; The piece he cut was 12.1 feet long.
Write a two-step equation to represent each problem:
A home repair crew charges seventy-five dollars per day plus two hundred fifty-five dollars for each hour the crew works. One day the crew works c hours and charges a total amount of one thousand, six hundred five dollars. How many hours does the crew work?
75 ?+ 255c = 1,605
Write an equation to represent the problem. Then solve:
The sum of 15 and two times a number is 29. What is the number?
15 ?+ 2y = 29; y = 7
APPLICATION OF PERCENT
Solve.
Joanna wants to buy a car. Her parents loan her $5,000 for 5 years at 5% simple interest. How much will Joanna pay in interest?
$1,250