Algebra 2 Word Problems?

Question

1) In a pair of complementary angles, one angle measures 18 degrees less than three times the other angle. Find the measure of each angle.

 

2) The speed of a commuter plane is 150 miles per hour slower than that of a passenger jet. The commuter plane travels 450 miles in the same time the passenger jet travels 1150. Find the speed of each aircraft.

 

3) The base of a triangle is four times height. The area of the triangle is 98 square centimeters. Find the dimensions of the triangle.

 

Thanks to anyone who responds! 

Answer 1

1)

 

Complementary angles add up to 90 degrees.

 

Angle 1 = x

Angle 2 = 3x - 18

 

 

Set up equation.

 

x + 3x - 18 = 90

4x - 18 = 90

4x = 108

 x = 27

 

 

Substitute this value of x into the angles.

 

Angle 1 = 27 degrees

Angle 2 = 63 degrees

 

 

2)

 

Set up an equation to represent speed.

 

Let x = speed of commuter plane in mph

Let y = speed of passenger jet in mph

 

x = y - 150         

 

Use the equation

 

x = d/t        and     y = d/t

 

where:

x = speed

y = speed

d = distance

t = time

 

 

Use this formula to find the speed of the commuter plane.

 

x = 450 / t

 

t = 450 / x

 

 

Use it again to find the speed of the passenger jet.

 

y = 1150 / t

 

t = 1150 / y

 

 

Since they travel at the same time,

 

t = 450 / x = 1150 / y

 

450 / x = 1150 / y

 

 

Solve for x from this equation

 

450 = (1150 / y)x

 

450 / (1150 / y) = x

 

450y / 1150 = x

 

(9y / 23) = x

 

 

Substitute this value of x into the equation coded in orange.

 

(9y / 23) = y - 150

 

 

Cross multiply.

 

9y = 23(y - 150)

9y = 23y - 3450

 

 

Subtract 23 on both sides of equation.

 

-14y = -3450

     y = 246.43

 

 

Substitute this value of y into the equation orange to find x.

 

x = 246.43 - 150

x = 96.43

 

 

The speed of the commuter plane is 96.43 mph.

The speed of the passenger jet is 246.43 mph.

 

 

This one was a tricky one. Hopefully, this solution helps here.

 

 

3)

 

The area of a triangle is  (base × height) / 2

 

Let height = x

Let base = 4x

Area = 98 cm²

 

 

Set up equation.

 

 

(4x * x) / 2 = 98

 

4x² / 2 = 98

 

 

Multiply both sides of equation by 2.

 

4x² = 196

 

 

Divide both sides of equation by 4

 

x² = 49

 

 

Square-root both sides of equation.

 

x = √(49)

x = 7

 

 

Substitute this value of x into the dimensions.

 

height = 7 cm

base = 28 cm