TRANSLATE THE SENTENCES TO EQUATION AND SOLVE

Translate to an algebraic equation and solve :

Problem 1 :

n divided by 8 is -16

Solution :

n/8 = -16

n = -16(8)

n = -128

Problem 2 :

n divided by six is -24

Solution :

n/6 = -24

n = 6(-24)

n = -144

Problem 3 :

m divided by -9 is -7

Solution :

m/-9 = -7

m = (-9)(-7)

m = 63

Problem 4 :

m divided by -7 is -8

Solution :

m/(-7) = -8

m = (-8)(-7)

m = 56

Problem 5 :

The quotient of f and -3 is -18

Solution :

f/(-3) = -18

f = (-3)(-18)

f = 54

Problem 6 :

The quotient of f and -4 is -20

Solution :

f/(-4) = -20

f = (-4)(-20)

f = 80

Problem 7 :

The quotient of g and twelve is 8

Solution :

g/12 = 8

g = (8)(12)

g = 96

Problem 8 :

 The quotient of g and nine is 14

Solution :

g/9 = 14

g = (14)(9)

g = 126

Problem 9 :

Three-fourths of q is 12

Solution :

3/4q = 12

q = (12×4)/ 3

q = 16

Problem 10 :

 Two-fifths of q is 20

Solution :

2/5 of q = 20

(2/5)q = 20

2q/5 = 20

q = (20×5)/2

q = 50

Problem 11 :

 Seven-tenths of p is -63

Solution :

7/10(p) = -63

p = (-63×10)/7

p = -90

Problem 12 :

Four-ninths of p is -28

Solution :

4/9(p) = -28

p = (-28×9)/4

p = -63

Problem 13 :

m divided by 4 equals negative 6

Solution :

m/4 = -6

m = (-6)(4)

m = -24

Problem 14 :

The quotient of h and 2 is 43

Solution :

h/2 = 43

h = (43)(2)

h = 86

Problem 15 :

 Three-fourths of z is the same as 15

Solution :

3/4z = 15

z = (15×4)/3

z = 20

Problem 16 :

The quotient of a and 2/3 is 3/4

Solution :

a/(2/3) = 3/4

a = (3×2)/(4×3)

a = 1/2

Problem 17 :

The sum of five-sixths and x is 1/2

Solution :

5/6 + x = 1/2

x = 1/2 – 5/6

x = -1/3

Problem 18 :

The sum of three-fourths and x is 1/8

Solution :

3/4 + x = 1/8

x = 1/8 – 3/4

x = -5/8

Problem 19 :

The difference of y and one-fourth is -1/8

Solution :

y – 1/4 = -1/8

y = -1/8 + 1/4

y = 1/8

Problem 20 :

The difference of y and one-third is -1/6

Solution :

y – 1/3 = -1/6

y = -1/6 + 1/3

y = 1/6

Problem 21 :

The temperature of dry ice is −109.3°F. This is 184.9°F less than the outside temperature. What is the outside temperature?

Solution :

The temperature of dry ice = −109.3°F.

Let x be the outside temperature.

x + 184.9 = -109.3

x = -109.3 - 184.9

x = -294.2

Problem 22 :

A company makes a profit of $1.38 million. This is $2.54 million more than last year. What was the profit last year?

Solution :

Let x be the amount in last year.

Profit = 1.38

x + 2.54 = 1.38

x = 1.38 - 2.54

x = -$1.16

Problem 23 :

The difference in elevation of a helicopter and a submarine is 18  1/2 meters. The elevation of the submarine is − 7  3/4 meters. What is the elevation of the helicopter?

Solution :

Let x be the elevation of helicopter.

Elevation of submarine = -7  3/4

x - (-7  3/4) = 18  1/2

x + 7  3/4 = 18  1/2

x + 31/4 = 37/2

x = 37/2 - (31/4)

x = (74 - 31)/4

x = 43/4

x = 10  3/4

So, the elevation of the helicopter is 10  3/4.

Problem 24 :

The total height of the Statue of Liberty and its pedestal is 153 feet more than the height of the statue. What is the height of the statue?

Solution :

Let x be the height of statue.

The total height of the Statue of Liberty + height of pedestal = 305 ft

Height of pedestal = x + 153

x + x + 153 = 305

2x + 153 = 305

2x = 305 - 153

2x = 152

x = 152/2

x = 76 ft

So, the heigth of statue is 76 ft.

Problem 25 :

Your first jump is 50 1/6 feet higher than your second jump. Your first jump reaches −200 2/5 feet. What is the height of your second jump?

Solution :

Let x be the height of the second jump.

First jump = x + 50  1/6

x + 50  1/6 = -200  2/5 feet

x + 301/6 = -1002/5

x = -1002/5 - 301/6

x = (-6012 - 1505)/30

x = -7517/30

x = -250  17/30 ft