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Statement Problems (Algebra)

Subject

Algebra

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Study Guide

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Statement Problems (Algebra)
1- Total sales of A in a day were $10 more than what B sold on the same day. If A sold
Merchandise worth $ 425, what was the sale of B?
Solution:
Let, B’s sales = x
Then A’s sales= x+10
x +10 = $425
x + 10 10 = 425 10
x = 415
B’s sale = $ 415 Answer
2- M and S together sold 60 cars. If M sold twice as many cars as S, how many cars each sold?
Solution:
Let, S sold cars = x
Then, M sold cars= 2x
Total sale of M and S = x + 2x
x + 2x = 60 cars
3x = 60 cars
3x/3 = 60/3
x= 20 cars
S (x) sold cars = 20 cars
M (2x) sold cars = 40 cars (20 *2)
3- The Weaving Department of a factory occupies 3.5 times as much floor space as the Shipping
Department. If the Weaving Department occupies 4,200 square feet, what is the space
occupied by the Shipping Department?
Solution:
Let, the floor space of Shipping Department = x
The floor space of Weaving Department = 3.5 x
3.5 x= 4,200 square feet
3.5 x/3.5= 4,200/3.5
x= 1200 square feet
Floor space of Shipping Department(x) = 1200 square feet
4-Heat and light together cost a company $1,080 for the month of January.If the consumption
for heating purposes is three times as much as light, how much each each expense cost to the
company?

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Solution:
Cost of heat and light for the of January = $1,080
Let consumption of light = x
Then , consumption of heat = 3x
x + 3x = $1,080
4x = $1,080
4x/4=$1080/4
X= $270
Light consumption expense = $270
Heat consumption expense = $810 ($270*3)
5-A group bonus is to be divided among four employees in the ratio of their basic salaries which
are in the ratio of 7, 4, 2 and 5 respectively. If a total bonus of $540 is to be divided among
them, what would each employee receive ?
Solution:
Total group bonus = $540
Ratio of basic salaries among four employees = 7 ,4,2,& 5
Total of ratio of employees = 7 + 4 + 2 +5
= 18
Bonus contribution of employee has ratio of 7 = $540/18 *7
= $210
Bonus contribution of employee has ratio of 4 = $540/18 *4
= $120
Bonus contribution of employee has ratio of 2 = $540/18 *2
= $60
Bonus contribution of employee has ratio of 5 = $540/18 *5
= $150
6- A laptop is sold for $1,500 . The gross profit is 2/3 of the cost , what are the cost and the gross
profit ?
Solution:
Sale price of laptop = $ 1,500
Gross profit = 2/3 of cost
Let cost of laptop = x
Gross profit = x * 2/3 or 2x/3
x + 2x/3 = $1,500
3x/3 + 2x/3 = $1,500
3x + 2x = $1,500 * 3
5x = $4,500

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x = $ 900
Cost of laptop = $900
Gross profit on sale of laptop ($900 * 2/3)= $600

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