WRITING EQUATIONS FROM VERBAL DESCRIPTIONS

Using the alphabet introduced for unknown value, we have to translate the verbal description (information) given in the question as mathematical equation.

In translation, we have to translate  the following English words as the corresponding mathematical symbols.

                                  of ----> x (multiplication)

am, is, are, was, were, will be, would be ----> = (equal)

Write equation for each of the following verbal descriptions.

Question 1 :

Eighteen more than the number n is 125.

Answer :

n + 18 = 125

Question 2 :

Twenty is 7 less than twice the number w.

Answer :

20 = 2w - 7

Question 3 :

Nine less than twice x is three more than x.

Answer :

2x - 9 = x + 3

Question 4 :

Eight less than four times the number c is twenty.

Answer :

4c - 8 = 20

Question 5 :

The sum of four consecutive integers is -54.

Answer :

Let x be the first integer. Then the four consecutive integers are

x, (x + 1), (x + 2), (x + 3) and (x + 4)

Given : The sum of four consecutive integers is -54.

x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = -54

Question 6 :

The sum of four consecutive odd integers is 296.

Answer :

Let m be the first odd integer. Then the four consecutive integers are

m, (m + 2), (m + 4), (m + 6)

Given : The sum of four consecutive odd integers is 296.

m + (m + 2) + (m + 4) + (m + 6) = 296

Question 7 :

The product of three consecutive odd integers is 693.

Answer :

Let y be the first odd integer. Then the three consecutive integers are

y, (y + 2), (y + 4)

Given : The product of three consecutive odd integers is 693.

y(y + 2)(y + 4) = 693

Question 8 :

The sum of three fourths of the number a and 24 is negative 9.

Answer :

Question 9 :

A number g is decreased by 23 and then multiplied by ½. The result is 8 more than twice the number g.

Answer :

Question 10 :

The quotient of p and q is twelve less than three times the sum of p and q.

Answer :

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