2.3 Simplifying algebraic expressions  (Page 3/3)

If four times a number is increased by fifteen, the result is five. What is the number?

1. Let ${\displaystyle x=}$
4. Check:
5. The number is .

When three times a quantity is decreased by five times the quantity, the result is negative twenty. What is the quantity?

1. Let ${\displaystyle x=}$
4. Check:
5. The quantity is .

If four times a quantity is decreased by nine times the quantity, the result is ten. What is the quantity?

1. Let ${\displaystyle y=}$
4. Check:
5. The quantity is .

When five is added to three times some number, the result is equal to five times the number decreased by seven. What is the number?

1. Let ${\displaystyle n=}$
4. Check:
5. The number is .

When six times a quantity is decreased by two, the result is six more than seven times the quantity. What is the quantity?

1. Let ${\displaystyle x=}$
4. Check:
5. The quantity is .

When four is decreased by three times some number, the result is equal to one less than twice the number. What is the number?

4. Check:

When twice a number is subtracted from one, the result is equal to twenty-one more than the number. What is the number?

The perimeter of a rectangle is 36 inches. If the length of the rectangle is 6 inches more than the width, find the length and width of the rectangle.

1. Let ${\displaystyle w=}$ the width.
   = the length.
2. We can draw a picture.
   
4. Check:
5. The length of the rectangle is inches, and the width is inches.

The perimeter of a rectangle is 48 feet. Find the length and the width of the rectangle if the length is 8 feet more than the width.

1. Let ${\displaystyle w=}$ the width.
   = the length.
2. We can draw a picture.
   
4. Check:
5. The length of the rectangle is feet, and the width is feet.

The sum of three consecutive integers is 48. What are they?

1. Let ${\displaystyle n=}$ the smallest integer.
   = the next integer.
   = the next integer.
4. Check:
5. The three integers are , , and .

The sum of three consecutive integers is -27. What are they?

1. Let ${\displaystyle n=}$ the smallest integer.
   = the next integer.
   = the next integer.
4. Check:
5. The three integers are , , and .

The sum of five consecutive integers is zero. What are they?

1. Let ${\displaystyle n=}$
5. The five integers are , , , , and .

The sum of five consecutive integers is -5. What are they?

1. Let ${\displaystyle n=}$
5. The five integers are , , , , and .

The perimeter of a rectangle is 18 meters. Find the length and width of the rectangle if the length is 1 meter more than three times the width.

The perimeter of a rectangle is 80 centimeters. Find the length and width of the rectangle if the length is 2 meters less than five times the width.

Find the length and width of a rectangle with perimeter 74 inches, if the width of the rectangle is 8 inches less than twice the length.

Find the length and width of a rectangle with perimeter 18 feet, if the width of the rectangle is 7 feet less than three times the length.

A person makes a mistake when copying information regarding a particular rectangle. The copied information is as follows: The length of a rectangle is 5 inches less than two times the width. The perimeter of the rectangle is 2 inches. What is the mistake?

A person makes a mistake when copying information regarding a particular triangle. The copied information is as follows: Two sides of a triangle are the same length. The third side is 10 feet less than three times the length of one of the other sides. The perimeter of the triangle is 5 feet. What is the mistake?

The perimeter of a triangle is 75 meters. If each of two legs is exactly twice the length of the shortest leg, how long is the shortest leg?

If five is subtracted from four times some number the result is negative twenty-nine. What is the number?

If two is subtracted from ten times some number, the result is negative two. What is the number?

If three less than six times a number is equal to five times the number minus three, what is the number?

If one is added to negative four times a number the result is equal to eight less than five times the number. What is the number?

Find three consecutive integers that add to -57.

Find four consecutive integers that add to negative two.

Find three consecutive even integers that add to -24.

Find three consecutive odd integers that add to -99.

Suppose someone wants to find three consecutive odd integers that add to 120. Why will that person not be able to do it?

Suppose someone wants to find two consecutive even integers that add to 139. Why will that person not be able to do it?

Three numbers add to 35. The second number is five less than twice the smallest. The third number is exactly twice the smallest. Find the numbers.

Three numbers add to 37. The second number is one less than eight times the smallest. The third number is two less than eleven times the smallest. Find the numbers.

( [link] ) Find the decimal representation of ${\displaystyle 0\text{.}\text{34992}÷4\text{.}\text{32}}$ .

( [link] ) A 5-foot woman casts a 9-foot shadow at a particular time of the day. How tall is a person that casts a 10.8-foot shadow at the same time of the day?

( [link] ) Use the method of rounding to estimate the sum: ${\displaystyle 4\frac{5}{\text{12}}+\text{15}\frac{1}{\text{25}}}$ .

( [link] ) Convert 463 mg to cg.

( [link] ) Twice a number is added to 5. The result is 2 less than three times the number. What is the number?