# MIXED OPERATIONS WORD PROBLEMS

In this section, you will learn,  how to solve word problems using two or more of the four binary operations (addition, subtraction, multiplication and division) in Math.

Problem 1 :

Gian asked Jessica to think of a positive number. Then, he asked her to divide the number by 4 and add 5 to it. Further he asked her to multiply it by 3 and subtract 7 from the result. If the final answer is 53, find the number that Jessica thought.

Solution :

Let x be the number Jessica thought.

3[(x ÷ 4) + 5] - 7 = 53

3[(x ÷ 4) + 5] = 60

Divide both sides by 3.

(x ÷ 4) + 5 = 20

Subtract 5 from both sides.

÷ 4 = 15

x/4 = 15

Multiply both sides by 4.

x = 60

The number that Jessica thought is 60.

Problem 2 :

I had \$5000. I donated half of it to a family. In the family, father took \$1250, donated \$250 to an orphanage and the divided the rest equally to his five sons. Find the share of each son.

Solution :

The share of each son :

= [(5000/2) - 1250 - 250] ÷ 5

= [2500 - 1250 - 250] ÷ 5

= 1000 ÷ 5

= \$200

Problem 3 :

Mac has \$1,200 and he divides it into three equal parts. Later, the first part is divided equally among five children and second part is divided equally among four brothers. How much money will each child and each brother get?

Solution :

Amount of money will each child get :

= (1200/3) ÷ 5

= 400 ÷ 5

= \$80

Amount of money will each brother get :

= (1200/3) ÷ 4

= 400 ÷ 4

= \$100

Problem 4 :

Richard has \$1,425 and he invested in stock. In one day, his money became 2.5 times of what he invested. The next day he got a profit of \$281 and later loss of \$153. Determine his present amount.

Solution :

Richard's  present amount :

= 2x1425 + 281 - 153

= 2850 + 281 - 153

= 3131 - 153

= \$2,978

Problem 5 :

Lily had \$50 and withdrew \$200 from her bank account. He bought a pair of trousers for \$36.50, 3 shirts for \$15.00 each, and 5 pairs of shoes for \$27.00 each. After having spent money for the above items, How much did she have left?

Solution :

The total amount of money that Lily had :

= 50 + 200

- \$250

The total amount of money that Lily spent for purchase :

= 36.50 + 3x15 + 5x27

= 36.50 + 45 + 135

= \$216.50

Amount of money Lily had left after purchase :

= 250 - 216.50

= \$33.50

Problem 6 :

A box with 4 pencils costs \$3 and a box with 5 pens costs \$7.50. Find the total cost of 2 pencils and 8 pens.

Solution :

Given : A box with 4 pencils costs \$3.

Cost of 4 pencils = \$3

Cost of 1 pencil = 3/4

= \$0.75

Given : A box with 5 pencils costs \$7.50.

Cost of 5 pens = \$7.50

Cost of 1 pen = 7.50/5

= \$1.50

The total cost of 2 pencils and 8 pens :

= 2(0.75) + 8(1.50)

= 1.50 + 12

= \$13.50

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