Solving an equation/integer operations
3x + 7=25
X=6
Solution:
Subtract 7 from both sides:
3x = 18
Divide both sides by 3:
x = 6
A jacket is on sale for 25% off. The original price is $60. What is the sale price?
✅ Answer: $45
Find 25% of $60:
0.25 × 60 = $15
Subtract from the original price:
60 - 15 = $45
A triangle has a base of 10 cm and a height of 6 cm. What is its area?
✅ Answer: 30 cm²
Formula:
Area = ½ × base × height
Plug in values:
Area = ½ × 10 × 6 = 30 cm²
If 5 pencils cost $3, how much do 8 pencils cost?
✅ Answer: $4.80
Set up a proportion:
5/3 = 8/x
Cross-multiply:
5x = 24
Solve:
x = 24 ÷ 5 = $4.80
A movie ticket costs $8.50. If 3 friends go to the movies and buy popcorn for $4.25 each, how much do they spend in total?
✅ Answer: $38.25
Ticket total:
3 × 8.50 = $25.50
Popcorn total:
3 × 4.25 = $12.75
Add together:
25.50 + 12.75 = $38.25
-4 × (3 - 7) + 2 × (-6)
✅ Answer: 4
Inside parentheses:
3 - 7 = -4
Multiply:
-4 × -4 = 16
2 × -6 = -12
Add:
16 + (-12) = 4
A jacket originally costs $80. It goes on sale for 25% off, and there's an additional 10% off the sale price. What is the final price?
✅ Answer: $54
First discount:
25% of 80 = 0.25 × 80 = $20
80 - 20 = $60
Second discount:
10% of 60 = 0.10 × 60 = $6
60 - 6 = $54
The area of a triangle is 60 cm² and the base is 10 cm. What is the height?
✅ Answer: 12 cm
Use the formula:
Area = ½ × base × height
Plug in what we know:
60 = ½ × 10 × h
60 = 5h
h = 60 ÷ 5 = 12 cm
In a class, the ratio of boys to total students is 3/8. If there are 18 boys, how many students are in the class?
✅ Answer: 48 students total.
8/3=18/x
Cross multiply:
3x=144⇒x=48
Maya buys a jacket that costs $120. The store offers a 15% discount. After the discount, she must pay 8% sales tax. What is the final price?
✅ Answer: $110.16
Discount:
15% of $120 = 0.15 × 120 = $18
Discounted price = 120 - 18 = $102
Sales tax:
8% of $102 = 0.08 × 102 = $8.16
Final price = 102 + 8.16 = $110.16
The temperature was -3°F in the morning. By noon, it rose 7°F, then dropped 10°F by night. What’s the temperature at night?
✅ Answer: -6°F
Start at -3 + 7 = 4°F (noon)
Then 4 - 10 = -6°F
A stock price increased from $120 to $150. What is the percent increase?
✅ Answer: 25% increase
Increase:
150 - 120 = $30
Percent increase:
(30 ÷ 120) × 100 = 25%
A triangle has a base of 5 ½ cm and a height of 4 ⅓ cm. What is the area?
✅ Answer: 11 11/12 cm²
Convert to improper fractions:
5 ½ = 11/2, 4 ⅓ = 13/3
Area = ½ × base × height:
½ × (11/2) × (13/3) = (1/2) × (143/6) = 143/12
Convert to mixed number:
143 ÷ 12 = 11 R11 → 11 11/12 cm²
A car travels 210 miles in 3.5 hours. At the same rate, how far can it travel in 5 hours?
✅ Answer: 300 miles
Find the unit rate (miles per hour):
210÷3.5=60 mph
Then:
60×5=300
A plumber charges $50 for the first hour and $30 for each additional hour. Another plumber charges a flat rate of $40 per hour. At how many hours will the second plumber be the better deal?
✅ Answer: After 2 hours, the second plumber is cheaper.
Let h = number of hours
Plumber 1: 50+30(h−1)
Plumber 2: 40h
Set the two costs equal:
50+30(h−1)=40h⇒
50+30h−30=40h⇒
20+30h=40h⇒
20=10h⇒
h=2
What number do you get when you subtract the sum of -5 and -8 from -2?
✅ Answer: 11
Sum:
-5 + (-8) = -13
Subtract:
-2 - (-13) = -2 + 13 = 11
After a 20% discount, a pair of shoes costs $72. What was the original price?
✅ Answer: $90
Let the original price be x
x - 0.20x = 0.80x = 72
x = 72 ÷ 0.80 = $90
Find the area of a triangle with a base of 7.8 m and a height of 4.2 m.
✅ Answer: 16.38 m²
Area = ½ × 7.8 × 4.2
7.8 × 4.2 = 32.76
½ × 32.76 = 16.38
A 5-foot-tall person casts a 6-foot shadow. At the same time, a tree casts an 18-foot shadow. How tall is the tree?
✅ Answer: The tree is 15 feet tall.
Set up a proportion:
5/6=h/18
Cross multiply:
5⋅18=6⋅h⇒90=6h
Divide:
h= 90/6=15
A diver starts at sea level and descends 15 feet per minute. After 6 minutes, he ascends 9 feet per minute for 4 minutes. What is his final depth?
✅ Answer: 54 feet below sea level
Descent: 6×−15=−90ft
Ascent: 4×9=+36ft
Final depth = -90 + 36 = -54 feet
(-2)² - 3 × (-4) + 6
✅ Answer: 22
Exponents first:
(-2)² = 4
Multiplication:
-3 × -4 = 12
Now compute:
4 + 12 + 6 = 22
A student estimated a book had 250 pages, but it actually had 200 pages. What is the percent error?
✅ Answer: 25%
Error = |250 - 200| = 50
Percent error = (50 ÷ 200) × 100 = 25%
A triangle has vertices at (1, 2), (5, 2), and (1, 6). What is its area?
✅ Answer: 8 square units
This is a right triangle with:
Base: from (1,2) to (5,2) → 4 units
Height: from (1,2) to (1,6) → 4 units
Area = ½ × base × height = ½ × 4 × 4 = 8
Two similar triangles have side lengths in a ratio of 2:52:52:5. If a side of the larger triangle is 15 cm, what is the length of the corresponding side in the smaller triangle?
✅ Answer: 6 cm
x/15 = 2/5
Cross multiply:
5x=30⇒x=6
Lena saved $300 from her birthday money. She decided to spend 25% on clothes, 10% on books, and save the rest in her bank account. After a month, she earned 10% interest on the amount she put in the bank. How much money does she have after one month, including interest?
Clothes:
25% of $300 = 0.25×300=75
Books:
10% of $300 = 0.10×30
Amount saved:
300 - 75 - 30 = $195
Interest earned:
10% of $195 = 0.10×195=19.5
Total after one month:
195 + 19.50 = $214.50