MODELING WITH LINEAR EQUATIONS WORD PROBLEMS WORKSHEET

Question 1 :

The scale reading, R(mm) when weights w (grams) are placed on a spring balance is given by the formula R  =  0.4w + 5.

Find w when :

(a) R  =  27      (b) R  =  42

Solution

Question 2 :

In the united states of America temperature is measured in degrees Fahrenheit (°F) rather than in degrees Celsius (°C). The rule showing the relationship between these two temperature scales is given by

F  =  1.8C + 32

What temperature in ˚C corresponds to a temperature of :

(a) 40°F     (b)  0°F     (c) 200°F

Solution

Question 3 :

The total cost $C, to sink a bore to given by the rule

C  =  15d + 350

where d is the depth in metres. How deep a bore can a farmer obtain for a cost of :

a) $2000    b) $3200

Solution

Question 4 :

Ben walks at a rate of 3 miles per hour. He run at a rate of 6 miles per hour. In one week, the combined distance that he walks and runs is 210 miles.

a) Write a linear model that relates the number of hours that Ben walks to the number of hours Ben runs.

b) Ben runs for 25 hours. For how many hours does he run ?

Solution

Question 5 :

A salesperson receives a base salary of $35000 and a commission of 10% of the total sales for the year.

a) Write a linear model that shows the salesperson’s total income based on total sales for k dollars.

b) If the salesperson sells $250000 worth of merchandise, what is her total income for the year, including her base salary ?

Solution

Question 6 :

Amery has x books that weigh 2 pounds each and y books that weigh 3 pounds each. The total weight of his books is 60 pounds.

a) Write a linear model that relates the number of 2 pound books to the number of 3 pound books Amery has.

b) If Amery has 10 3-pound books, how many 2 pound books does he have ?

Solution

Answers :

(1)  (a)  w  =  55 g  (b)  w  =  92.5 g

(2)  (a)  C  =  4.44˚C    (b)  -17.8˚C     (c)  93.3˚C

(3)  (a)  d  =  110 m   (b)  d  =  190 m

(4)  (a)  3x + 6y  =  210   (b)  x  =  20 hrs

(5)  (a)  y  =  0.1k + 35000   (b)  y  =  $60000

(6)  (a)  2x + 3y  =  60    (b)  x  =  15

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