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Writing Equations
Consecutive Integers
Perimeter Problems
Distance-Rate-Time Problems
Transforming Formulas
100
Six less than a number is -32. What is the number?
n - 6 = -32
n = -26
100
Find two consecutive integers whose sum is 123.
1st integer: n
2nd integer: n+1
n+n+1=123
The two numbers are 61 and 62.
100
The length of a rectangle is 4 inches more than its width. The perimeter is 96 inches. Find the length and width of the rectangle.
width: w
length: w+4
2w+2(w+4) = 96
width = 22 inches, length = 26 inches
100
Complete the distance formula.
d = ?
d = rt
100
The formula A = bh can be used to find the area of a parallelogram (A), given the base (b) and the height (b).
Transform the formula to solve for b, then use this to find the base of a parallelogram with an area of 47.73 square cm and a height of 12.9 cm.
A/h = b
base = 3.7 cm
200
Eight less than 7 times a number is -29.
7n - 8 = -29
n = -3
200
Find two consecutive even integers whose sum is 54.
1st integer: n
2nd integer: n+2
n+n+2=54
The two integers are 26 and 28.
200
The length of a rectangle is 6 times its width. The perimeter of the rectangle is 98 feet. Find the length and width of the rectangle.
width: w
length: 6w
2w+2(6w) = 98
width = 7 feet, length = 42 feet
200
A passenger plane made a trip to Las Vegas and back. On the trip there it flew 432 mph and on the return trip it went 480 mph. How long did the trip there take if the return trip took nine hours?
The trip there took 10 hours.
200
The formula P = 2l + 2w can be used to find the perimeter of a rectangle (P), given the length (l) and the width (w).
Transform the formula to solve for w, then use this to find the width of a rectangle with a perimeter of 50 inches and a length of 18 inches.
(P-2l)/2 = w OR P/2 - l
The width is 7 inches.
300
Six less than two-thirds of a number is negative ten. Find the number.
2/3n - 6 = -10
n = -6
300
Find three consecutive odd integers whose sum is −45.
1st integer: n
2nd integer: n+2
3rd integer: n+4
n+n+2+n+4 = -45
The three integers are -13, -15, and -17.
300
An equilateral triangle is a triangle in which all the sides are equal. If the perimeter of an equilateral triangle is 27 inches, how large is each side of the triangle?
side: s
s + s + s = 27
each side is 9 inches
300
Linda left home and drove for 2 hours. She stopped for lunch then drove for another 3 hours at a rate that is 10 mph higher than the rate before she had lunch. If the total distance Linda traveled is 230 miles, what was the rate before lunch?
40 mph
300
The formula V = lwh can be used to find the volume of a rectangular prism (V), given the length (l), width (w), and height (h).
Transform the formula to solve for l, then use this to find the length of a rectangular prism with a volume of 918 cubic feet, a width of 9 feet, and a height of 17 feet.
V/wh = l
The length is 6 feet.
400
When 7 times a number is decreased by 8, the answer is the same as when 3 times the number is increased by 4. Find the number.
7n - 8 = 3n + 4
n = 3
400
Three consecutive odd integers are such that the sum of the first and the third is 70. Find the integers.
1st integer: n
2nd integer: n+2
3rd integer: n+4
n+n+4 = 70
The integers are 33, 35, and 37.
400
An isosceles triangle is a triangle in which two of the sides are equal. If each of the equal sides of an isosceles triangle is 5 times the third side and the perimeter of the triangle is 121 inches, how many inches is each of the sides of the triangle?
equal sides: 5s
third side: s
5s + 5s + s = 121
The two equal sides are 55 inches and the third side is 11 inches.
400
Kali left school and traveled toward her friend's house at an average speed of 40 km/h. Matt left one hour later and traveled in the opposite direction with an average speed of 50 km/h. Find the number of hours Matt needs to travel before they are 400 km apart.
4 hours
400
The formula S = (n - 2)180. can be used to find the sum of interior angles (S) for a polygon with (n) sides.
Transform the formula to solve for n, then use this to find the number of sides a polygon has if the sum of its interior angles is 900 degrees.
n = (S/180) + 2
The polygon has 7 sides..
500
The larger of two numbers is 10 more than the smaller number. Five times the larger number is 40 more than 6 times the smaller. Find the numbers.
smaller #: n
larger #: n+10
5(n+10) = 6n + 40
The numbers are 10 and 20.
500
Three consecutive even integers are such that the sum of the smallest and 3 times the second is 38 more than twice the third. Find the integers.
1st integer: n
2nd integer: n+2
3rd integer: n+4
n+3(n+2) = 2(n+4) + 38
The integers are 20, 22, and 24.
500
The shorter side of a triangle is 5 inches less than the medium size side. The larger side is 12 inches more than the medium size side. If the perimeter of the triangle is 40 inches, find the size of each side of the triangle.
medium side: m
shorter side: m - 5
larger side: m + 12 m + m - 5 + m + 12 = 40
The three sides are 6 inches, 11 inches, and 23 inches
500
At 9 am a car (A) began a journey from a point, traveling at 40 mph. At 10 am another car (B) started traveling from the same point at 60 mph in the same direction as car (A). At what time will car B pass car A?
12:00 PM
500
The formula V = πr²·h can be used to find the volume of a cylinder (V), given the radius (r) and height (h).
Transform the formula to solve for r, then use this to find the radius of a cylinder with a volume of 461.58 cubic cm and a height of 3 cm. (Use 3.14 for pi)
√[V/(π·h)] = r
The radius is 7 cm.