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I did it by trial & error

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The formula is

For 5 year investment:
yrs
(semi-annually)




------------------------
For 3 year investment:

(quarterly)





------------------------------
If I read the problem right, , the earnings
after 5 years, will become , the principle
invested for 3 years
given:


--------------------
substituting:



and





The original principle invested is $12,264.76
Hope I got it right

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Let = weekly income

Remaining is
25% of is
given:
is subtracted from weekly income






Weekly income is RS800

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answer
I can check this answer on my calculator



and


I think I made a rounding-off error, but
answer must be OK

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Get both equations in the form
and if the 's are the same, they are parallel
(they are)

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Let = number of nickels
Let = number of dimes
Let = number of quarters
given:
(1) (in cents)
(2)
There are 3 unknowns, and only 2 equations,
so it will take some extra work to solve
Substitute (2) into (1)


cents
Now just use logic
There can't be 5 quarters, since that's more than
There can't be 4 quarters, since



(can't have 1/2 dime)
I'll try 3 quarters



(can't have 4/3 dimes)
I'll try 2 quarters



(can't have 13/6 dimes)
And 1 quarter



and, since
(2)


There is 1 quarter, 3 dimes, and 11 nickels
check:
(1)



OK

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answer
I just factored it in my head, but completing
the square works, too

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Multiply both sides by



The length of the shadow is 4.08 ft

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Call the consecutive odd integers and
given:

---------------



The smallest integer is 121
check:

OK

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what are the units of 2745 ?

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Age of her car now =
Age of his car now =
Age of her car 3 years ago =
Age of his car 3 years ago =
given:
(1)
(2)
---------------
from (12),

from (2),
(2)


and



Her car is 7 years old and his car is 5 years old

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Let = the original price
given:




The original price was $15,737.50

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I write 2 equations, 1 for each trip


given:
mi
mi
mi/hr
(10 min is 1/6 hr)
------------------
given:

(1)
and


------------------
(2)
Substitute (1) in (2)

Subtract from both sides

Multiply both sides by

and, from (1)


Multiply both sides by


Use quadratic equation









(the negative answer is impossible)



The speed on the return trip is 56 mi/hr
check answer:
(1)

-----------------------

hr (1 hr 10 min)
and





hr
OK

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The factors are:
and

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In order to be a function, each must match with a single
. In the 1st case, , and there can only be
one for each .
In the 2nd case, , and
Each matches with 2 values of
Here's a graph of each. The curve on the right is not a function

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Let = Tim's age
Let = Jenny's age
Let = Ellen's age
given:



By substitution,

Multiply both sides by



and, since



Tim is 8 years old
check:



and



OK

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I can write 2 equations, 1 for each vehicle

and

---------------
given:
mi/hr
hrs
hrs
mi
---------------
Now I plug in the substitutions



(1)
and

(2)
Substitute (2) in (1)
(1)

mi/hr
and, since


mi/hr
The rate of the car is 50 mi/hr
check:




mi
and



In 2 hours, the car is 20 mi ahead of the bus
OK

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If a line has slope = , then
any line perpendicular to it will have
slope =


Perpendicular line J,

So far I know line J has the form
. I know it goes through (1,1),
so I can just plug these values for and
back into the equation for J



The equation for J is
I'll plot the 2 lines to check my work

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Imagine that the sides are connected at one end and laying
right on top of eachother. Then imagine that one of the sides
is rotated a tiny fraction of a degree. The sides are now
, , and plus a tiny length.
Arranged this way, the 3rd side can't be smaller than cm
---------------------------------------------------------------
Now leave the given sides connected at one end, but rotate them
so they are 180 degrees opposite eachother. They now add up to
. Now rotate one of the sides a tiny fraction
of a degree. The sides are now {, , and
minus a tiny length.
Arranged this way, the 3rd side can't be greater than cm
----------------------------------------------------------------
The 3rd side has to be in this range, 3 cm to 7 cm

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Let = the original price of the knife
given:
The discount =
The discounted price =
dollars




Lucy saved $55.56

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What you have to do is try to express and in
terms of cubes. You can use a calculator or just play with numbersd
until you hit on the answer. Rewrite the equation like this:


Rewrite again

Rewrite again


answer
check answer:

Take the square root of both sides

Cube both sides

OK

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Let = number of incorrect answers
Then = number of correct answers
given:





I got 105 correct

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Another way to ask the question is:
"What number divided by and
multiplied times will give me
?

Multiply both sides by



is 12% of
check:


OK

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With these box problems, what they do,
usually, is cut small squares out of the corners
and then fold up the 4 equal height sides to
make the box.
So, I'll say that each of these 4 equal squares will have
dimensions cm2
To get the area of the bottom after the sides are
folded up, I subtract from each side.





Use the quadratic formula











and


(can't be answer, too big)
The box has to be 4 cm deep
check answer:





OK

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Let = number of student tickets sold
Let = number of adult tickets sold
given:
(1)
(2)
Multiply both sides of (1) by and
subtract (1) from (2)
(2)
(1)


and, since
(1)
(1)


125 student tickets and 325 adult tickets were sold
check:
(2)
(2)


OK

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Just looking at the units:
(miles/year) / (miles/gallon) = (miles/year) x (gallons/mile) = gallons/year
given:
She drives miles/year
Her present car gets miles/gallon
gallons/year
The car she wants gets miles/gallon
gallons/year
and
Gas is $/gallon for the year
For old car:
gallons/year x dollars/gallon = dollars/year
For new car:
gallons/year x dollars/gallon = dollars/year

In the 1st year, she'll save $206.25

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In words:
(quarts of pure grape juice at end)/(total quarts of drink at end) = 40%
given:
Let = quarts of pure grape juice to be added
In quarts of drink, I have
quarts pure grape juice
-----------------------------------------






2.5 quarts of pure grape drink must be added
check:





OK

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Write a separate equation for each
part of the trip
upstream:

(1) mi
downstream:

(2) mi
also:
(I'll call them both )
hrs
hrs
--------------------------
(1)
(2)
(2)
Subtract (1) from (2)



hrs
and, since



-----------------------
(1)

mi
and


mi
Both distances are the same, as they should be
Mark rowed mi

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Let = grams of 45% mixture to be used
Let = grams of 75% mixture to be used
given:
(1) grams
(2) = pure nickel in final mixture
------------------------------
In words:
( grams of pure nickel in final mixture )/(total grams) = 65%


(3)
Multiply both sides of (1) by and subtract
(1) from (3)
(3)
(1)


And, since



20 grams of the 45% mixture and 40 grams of the 75% mixture are needed
check:





OK

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40%