Solving Systems
x+y=10
x-y=4
x=7
y=3
A movie theater sells adult tickets for $12 each and child tickets for $8 each. One day, the theater sold a total of 50 tickets and collected $520. How many adult tickets and how many child tickets were sold?
30 adult tickets
20 child tickets
(3.0 × 10⁻⁵)(2.0 × 10⁻³)
6.0 × 10⁻⁸
(3x² − 5x³y + 6x²) + (−4x³y + 2x² − 9x³y)
11x² − 18x³y
(2x − 5)(x + 3)
2x² + x − 15
3x+2y=16
x+y=7
x=2
y=5
A coffee shop sells regular coffee for $3 per cup and specialty coffee for $5 per cup. One morning, they sold a total of 40 cups of coffee and made $156. How many cups of each type of coffee did they sell?
22 regular coffees
18 specialty coffees
(4.5 × 10⁻⁷)(3.2 × 10⁻⁴)
1.44 × 10⁻¹⁰
(2a³b − 6a²b² + 4ab³) + (5a²b² − 3a³b + 8ab³)
−a³b − a²b² + 12ab³
(3a + 2)(2a − 4)
6a² − 8a − 8
3x+2y=19
2x+3y=16
x=5
y=2
A family bought furniture in two different states. The furniture cost in the second state was $200 less than in the first state. The sales tax in the first state was 6%, and the sales tax in the second state was 8%. The total sales tax paid for both purchases was $94. How much did the furniture cost in each state before tax?
First state: $600
Second state: $500
(6.8 × 10⁻⁶)(2.5 × 10³)1.7 × 10⁻²
1.7 × 10⁻²
(−3x³y²z⁴)(2xy⁴z²)²
−12x⁵y¹⁰z⁸
(6n − 5)(2n + 3)
12n² + 8n − 15
3x + 4y = 18
5x - 2y = 4
x=2
y=3
Two trains leave a station at the same time and travel in opposite directions. One train travels 10 mph faster than the other. After 2 hours, the trains are 180 miles apart. What is the speed of each train?
Slower train: 40 mph
Faster train: 50 mph
(7.2 × 10⁴)(4.8 × 10⁻⁹)
3.456 × 10⁻⁴
(−5m⁴n³p²)(3m²n⁵p)³
−135m¹⁰n¹⁸p⁵
(3x + 2)(x² + 4x − 5)
3x³ + 14x² − 7x − 10
3x-4y=1
2x+3y=12
x=3
y=2
Two cars leave a parking lot at the same time and travel in opposite directions. One car travels 15 mph faster than the other. After 4 hours, the cars are 420 miles apart. What is the speed of each car?
Slower car: 45 mph
Faster car: 60 mph
(8.75 × 10⁶)(3.6 × 10⁻¹¹)
3.15 × 10⁻⁴
(2a⁻²b³ / 3a⁴b⁻¹)⁻²
9a¹² / 4b⁸
(2x − 3)(4x² − 5x + 6)
8x³ − 22x² + 27x − 18