Answer:
1. won 50 games and lost 32 games
2. 233 Democrats and 202 Republicans
3. 360 miles
4. 6 hours
5. 18 miles
Step-by-step explanation:
Question 1
- let x = number of games lost
- let y = number of games won
From the given information:
- Equation 1: x + y = 82
- Equation 2: x = y - 18
Substitute Equation 2 into Equation 1 and solve for y:
⇒ y - 18 + y = 82
⇒ 2y - 18 = 82
⇒ 2y = 100
⇒ y = 50
Substitute found value of y into Equation 2 and solve for x:
⇒ x = 50 - 18
⇒ x = 32
Therefore, the team won 50 games and lost 32 games.
Question 2
- let d = number of Democrats
- let r = number of Republicans
From the given information:
- Equation 1: d + r = 435
- Equation 2: d = r + 31
Substitute Equation 2 into Equation 1 and solve for d:
⇒ r + 31 + r = 435
⇒ 2r + 31 = 435
⇒ 2r = 404
⇒ r = 202
⇒ d = 233
Substitute found value of d into Equation 2 and solve for r:
⇒ 233 = r + 31
⇒ r = 202
Therefore, there were 233 Democrats and 202 Republicans.
Question 3
Given:
Distance (d) = vt
⇒ d = 180 × 2
⇒ d = 360 miles
Question 4
Given:
Time (t) = d ÷ v
⇒ t = 420 ÷ 70
⇒ t = 6 hours
Question 5
- Let c = velocity of car
- Let b = velocity of bus
If the velocity of the bus is 12 mph less than the car then:
⇒ c = b + 12
Given journey times:
- Car: t = 30 mins = 0.5 h
- Bus: t = 45 mins = 0.75 h
Distance (d) = vt
Create two equations for distance:
Bus
⇒ d = b × 0.75 = 0.75b
⇒ d = 0.75b
Car
⇒ d = (b + 12) × 0.5
⇒ d = 0.5b + 6
Distance for both vehicles is the same. Equate the two equations for d and solve for b (velocity of bus):
⇒ d = d
⇒ 0.75b = 0.5b + 6
⇒ 0.25b = 6
⇒ b = 24 mph
Substitute the value of b into one of the distance formulas and solve for d:
⇒ d = 0.5(24) + 6
⇒ d = 18 miles
