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r Peter can mow the lawn in 40 minutes and John can mow the lawn in 60 minutes. How long will it take
for them to mow the lawn together?
Solution: Let ÿ time to mow lawn together
Answer: The time taken for both of them to mow the lawn together is 24 minutes.
Jane, Paul and Peter can finish painting the fence in 2 hours. If Jane does the job alone she can
finish it in 5 hours. If Paul does the job alone he can finish it in 6 hours. How long will it take for
Peter to finish the job alone?
Solution: Let ÿ time taken by Peter
Answer: The time taken for Peter to paint the fence alone is hours
Î
John¶s father is 5 times older than John and John is twice as old as his sister Alice. In two years time,
the sum of their ages will be 58. How old is John now?
Let ÿ be John¶s age now.
r
John¶s father 5x 5x+2
John x x+2
Alice
Answer: John is now 8 years old.
r Pey is twice as old as his friend Poy. Poy is 5 years older than Jaz. In 5 years, Pey will be three times
as old as Jaz. How old is Poy now?
Let ÿ be Poy¶s age now.
Pey 2x 2x + 5
Poy x x+5
Jaz x-5 x -5 +5
2ÿ + 5 3(ÿ ± 5 + 5)
2ÿ + 5 3ÿ
ÿ5
Answer: Poy is now 5 years old.
Frances is 10 years old and his brother is 2 years old. In how many years will Frances be twice as old
as his brother?
Frances 10 x + 10
Brother 2 x+2
ÿ + 10 2(ÿ + 2)
ÿ + 10 2(ÿ + 2)
ÿ + 10 2ÿ + 4
6ÿ
ÿ6
So in 6 years Frances will be twice as old as his brother.
Forty less than five times a number of fifty-two less than the number. Find the number.
SOLUTION:
5x ± 40 x ± 52
5x ± x -40 x ± x ± 52
4x ± 40 -52
4x ± 40 + 40 -52 + 40
4x -12
ü Ô
ü
ü
X -3
r Twice the sum of a number and six is two more than three times the number. Find the number.
SOLUTION:
Let x represent the unknown number.
2(x + 6) 3x + 2
2x + 12 3x + 2
2x ± 2x + 12 3x ± 2x ± 2
12 x + 2
12 ± 2 x + 2 ± 2
10 x
T he sum of two consecutive odd integers is -188. Find the integers.
SOUTION:
x(x+2) -188
2x + 2 -188
2x + 2 ± 2 -188 ± 2
2x -190
Ô
x -95
Mari has 20 ounces of a 20% of salt solution, How much salt should he add to make it a 25% solution?
Original Added Result
concentration 0.2 1 0.25
amount 20 x 20 + x
Multiply 0.2 x 20 1 (x) 0.25(20 + x)
.2 × 20 + 1 × ÿ 0.25(20 + ÿ)
4 + ÿ 5 + 0.25ÿ
ÿ ± 0.25ÿ 5 ± 4
0.75ÿ 1
Answer: He should add ounces of salt.
r 0harllote Besch is a chemist. She needs a 20% solution of alcohol. She has a 15% solution on
hand as well as a 30% solution. How many liters of the 15% solution should she add to 3L of the
30% solution to obtain her 20% solution?
LET x : number of liters of 15% solution to be added
Strength Liters of solution Liters of pure alcohol
15% x .15x
30% 3 30(3)
20% 3+x .20( 3 + x)
.15 + .30(3) .20 (3 + x)
.15x + .90 .60 + . 20x
.15x - .20x .60 - .90
.05x .30
Ë
Ë
Ë
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x6
She has 10 pounds of $3 coffee for a total worth of $30 and x pounds of $5 coffee. The question asks
of how much of the x $5 coffee is needed to mix with the 10 pounds of $3 coffee to make (10 + x) pounds
of $4.50 coffee with a total value of $4.50 * (10 + x)
to set this up we would then have:
3(10) + 5x (10 + x) * 4.50
30 + 5x 45 + 4.50 x *multiply by 100 to get rid of decimal
3000 + 500x 4500 + 450x
50x 1500
x 1500/50
x 30
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Last month, Zainal earned P500. This month he earned P520. 0alculate the percentage
increase in his earnings.
m
Increase P520 ± P500 P20
Percentage increase
The percentage increase in his earnings is 4%.
r chat is the percentage increase from 25 to 29.5?
m
Increase 29.5 ± 25 4.5
Percentage increase
Last month, Mhie earned P500. This month he earned P450. 0alculate the percentage decrease
in his earnings.
m
Decrease P500 ± P450 P50
Percentage decrease
The percentage decrease in his earnings is 10%.
