SOLVING EQUATIONS QUESTIONS AND ANSWERS

Question 1 :

Solve for a.

a + (-11) = -25

Answer :

a + (-11) = -25

a - 11 = -25

Add 11 to both sides.

a = -14

Question 2 :

Solve for y.

-24 = 8y

Answer :

-24 = 8y

Divide both sides by 8.

-3 = y

Question 3 :

Solve for x.

Answer :

3x - 10 = 95

3x = 105

x = 35

Question 4 :

-11 + x = 9

Given the above equation, find the value of 20 - (11 - x).

Answer :

-11 + x = 9

Add 11 to both sides.

x = 20

The value of 20 - (11 - x) :

= 20 - (11 - 20)

= 20 - (-9)

= 20 + 9

= 29

Question 5 :

If 33 - a = a + 27 - 5a, what is the value of 33 + 3a?

Answer :

33 - a = a + 27 - 5a

33 - a = 27 - 4a

Add 4a to both sides.

33 + 3a = 27

Question 6 :

Answer :

The two different denominators in the above equation are 2 and 4.

The least common multiple of (2, 4) = 4.

Multiply both sides of the equation by 4, to get rid of the denominators.

Question 7 :

If x - (3 - 2x) + (4 - 5x) = -7, what is the value of x?

Answer :

x - (3 - 2x) + (4 - 5x) = -7

x - 3 + 2x + 4 - 5x = -7

-2x + 1 = -7

-2x = -8

x = 4

Question 8 :

If three quarters of a number decreased by twenty is equal to eighty two, what is that number?

Answer :

Let x be the required number.

Multiply both sides by 4 to get rid of the denominator 4 on the left side.

3x - 80 = 328

3x = 408

x = 136

Therefore, the number is 136.

Question 9 :

Two and three fifths of a number equals -26. What is the number?

Answer :

Let x be the required number.

Therefore, the number is -10.

Question 10 :

There are one hundred forty-two students in a high school band. These students represent two ninth of the total students in the high school. How many students attend the school?

Answer :

Let x be the total number of students in the school.

Given : There are one hundred forty-two students in a high school band. These students represent two ninth of the total students in the high school.

2x = 1278

x = 639

Therefore, 439 students attend the school.

Question 11 :

820c + 380r = 4360

The above equation models the amount of calories in a snack of c cups of cashews and r cups of raisins. The amount of calories per cup of cashews is 820 and the amount of calories per cup of raisins is 380. According to the equation, how many cups of raisins are used, if 3 cups of cashews are used to make the snack?

Answer :

If the number of cashews is 3, we have to find the number of cups of raisins.

820c + 380r = 4360

Substitute c = 3.

820(3) + 380r = 4360

2460 + 380r = 4360

380r = 1900

r = 5

If 3 cups of cashews are used, 5 cups of raisins are used.

Question 12 :

What number increased by ¼ of itself is equal to 30?

Answer :

Let x be the required number.

Given : The number increased by ¼ of itself is equal to 30.

Therefore, the number is 24.

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