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Please answer all of theses asap

Please answer all of theses asap-example-1

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Answer:

1. won 50 games and lost 32 games

2. 233 Democrats and 202 Republicans

3. 360 miles

4. 6 hours

5. 18 miles

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:

  • v = 180 m/h
  • t = 2 h

Distance (d) = vt

⇒ d = 180 × 2

⇒ d = 360 miles

Question 4

Given:

  • v = 70 mi/h
  • d = 420

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

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