Solve the Equation
If 2 is subtracted from a number, the result is 4. Determine the number.
x -2 = 4
x = 6
Lin is tracking the progress of her plant’s growth. Today the plant is 5 cm high. The plant grows 1.5 cm per day. What will the height of the plant be after 20 days?
5 + 1.5day = height
5 + 1.5(20) = height
5 + 30 = height
35
The difference of two numbers is 3. Their sum is 13. Write the equations.
a - b = 3
a + b = 13
The sum of 8 and 5 is equal to the difference of number and 7. Determine the number.
8 + 5 = n - 7
13 = n -7
13 + 7 = n
20 = n
Mr. Thompson is on a diet. He currently weighs 260 pounds. He loses 4 pounds per month. After how many months will Mr. Thompson reach his goal weight of 220 pounds?
260 - 4*month = weight
260 - 4m = 220
-4m = 220 - 260
-4m = -40
m = -40/-4
m = 10
The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Write the equations.
3s + 1c = 38
3s + 2c = 52
Five less than 2 times a number is 7. Determine the number.
2n - 5 = 7
2n = 7 + 5
2n = 12
n = 12/2
n = 6
A salesperson receives a base salary of $35,000 and a commission of 10% of the total sales for the year. If the salesperson sells $250,000 worth of merchandise, what is her total income for the year, including her base salary?
35,000 + .1(250,000) = income
35,000 + 25,000 = income
60,000 = income
The state fair is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 8 vans and 8 buses with 240 students. High School B rented and filled 4 vans and 1 bus with 54 students. Every van had the same number of students in it as did the buses. Write the equations.
8v + 8b = 240
4v + 1b = 54
The sum of 9 and the quotient of x and 7 is 11
x/7 = 11-9
x/7 = 2
x = 2 * 7
x = 14
The population of Bay Village is 35,000 today. Every year the population of Bay Village increases by 750 people. In approximately many years will the population of Bay Village exceed 50,000 people?
35,000 + 750 * year = population
35,000 + 750 * year > 50,000
750y > 50,000 - 35,000
750y > 15,000
y > 15,000/750
y > 20
21 years
A boat traveled 336 miles downstream and back. The trip downstream took 12 hours. The trip back took 14 hours. Write equations with variables for the speed of the boat in still water and the speed of the current.
336mi/12hr = boat + current
336mi/14hr = boat - current
The opposite of the sum of 5x and 10 is equal to the product of x and 15
-(5x + 10) = 15x
-5x - 10) = 15x
-10 = 15x + 5x
-10 = 20x
-10/20 = x
-12 = x
A Pizza restaurant offers the following deals:
Deal #1: $8.99 for one large pizza and $5 for each additional large pizza on the same order
Deal#2: $6.00 per large pizza
At what number of pizzas does Deal #1 become a better deal?
Deal 1: 8.99 + 5 (pizza - 1)
Deal 2: 6 * pizza
8.99 + 5(p-1) < 6p
8.99 + 5p - 5 < 6p
3.99 + 5p < 6p
3.99 < 6p - 5p
3.99 < p
4 pizzas
The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9. Write the equations.
a + b = 7
10b + a = 10a + b + 9