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| ALGEBRA
- solved problems |
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Linear
equations
in one variable
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Miscellaneous word
problems
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| 147. |
If fresh grapes contain 90% water and dried 12%, how much dry grapes we get from 22 kg of fresh
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| grapes?
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Solution:
Fresh grapes contain 90% water and 10% dry substance.
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Dry grapes contain 12% water and 88% dry substance.
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of dry grapes, so |
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| 148. |
An amount decreased 20% and then increased 50%, what is the total increase in relation to initial
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Solution: An initial amount
x decreased by 20%, |
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The obtained amount increased by 50%, |
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The difference in relation to the initial value x,
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shows increase by 20%.
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| 149. |
From a total deducted is 5% for expenses and the remainder is equally divided to three persons.
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What was the total
if each person gets $190?
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Solution: If
x
denotes the total then |
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| 150. |
Into 10 liters of the liquid
A poured is 4 liters of the liquid
B
and 6 liters of the liquid
C.
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From obtained mixture D
poured is out 3 liters, how many liters of the liquid C
remains in the mixture
D?
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Solution:
A
+ B
+ C
= D =>
10 l + 4 l + 6 l = 20 l
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| Variable expressions
(expressions involving variables) and formula problems |
| Solving
a formula for a specified variable, transposition of a
formula (changing the subject of
a formula) |
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| 151. |
Into a cistern are poured 37.4 tonnes of petrol and remains 6.5% of the cistern not filled.
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| How many tonnes of the petrol will fit in the cistern to be full.
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Solution:
Applying the
proportion B :
A
=
100% :
p,
where
A = 37.4 tonnes or 93.5%
denotes the amount (that
correspond to percentage), B
is base (correspond
to the whole or 100%) and p
is percent, it follows that
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| 152. |
Fresh figs contain 90%
of water and dry figs contain 12%. How many kilos of dry figs are obtained
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by drying 264 kg of fresh
figs?
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Solution:
Using the
proportion B
:
(B
± A)
= 100 :
(100
± p),
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As fresh figs contain 10% of the dry substance and dry figs contain 88% of the dry
substance it follows that 264 kg of fresh figs contains 26.4 kg of the dry substance.
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weight of the dry figs decreased by 12% of water, so B -
A = 26.4 kg,
and by using the above formula |
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| obtained
is the
weight of the dry figs. |
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| 153. |
Sum of all three-digits numbers divisible by 3 is?
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Solution: The
three-digits numbers divisible by 3
are;
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102, 105, 108,
. . . , 996, 999
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they represent the arithmetic
progression |
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a1,
a2,
a3,
¼
, an
- 1,
an,
where a1
= 102, an
= 999 and d
= 3, |
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an
= a1 + (n - 1)
· d then 999
= 102 + (n - 1)
· 3
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3
· (n - 1)
= 897 | ¸3
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- 1
= 299
=> n
=
300 |
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sum formula, |
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| 154. |
How many minutes pass while watch hands coincide again?
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Solution: Suppose watch hands last coincide at noon. They will
coincide again 5 to 6 minutes after 13 hours.
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| To reach 13 hours, the minute hand traveled full circle 360° or 60 minutes,
and the hour hand traveled 30°.
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Therefore, the minute hand travels at speed of |
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degrees per minute, |
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degree per minute. |
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Hands will coincide again the minute hand passes additional distance of
30° +
x° while, at the same time, the hour hand passes the distance of
x°, i.e.,
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| Thus, watch hands will coincide again after
60 min + 5 min + 5/11 min = 65 and 5/11 min. |
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If v = g t + v0
and |
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then t is
equal?
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