Pls.tell me what's the formula?

Question

1) The average of 2 numbers is 70.If the difference between them is 12,what is the smaller number?
2) The average height of 5 boys is 1.15.If one boy is 1m 62cm tall,what is the average height of the other 4 boys?
3) The taxi driver charges $2.60 for the first km and 10 cents per additional 200m.How much must a passenger pay for a journey of 12 km?
4) Find the cost of fencing four sides of a rectangular fielf that measures 12.78m by 10 m at $25 per metre.

Pls tell me how to solve by giving me some formula!!!Thanks

Answer 1

the only formula you need is the formula for "average"

average = 1/N x (sum of N values)


the rest is logic and common sense.

Answer 2

1.) (X + Y) / 2 = 70

X - Y = 12

Those are the two given statements.
So let's begin with the first one...

(X + Y) / 2 = 70 mult both sides by 2
(X + Y) = 140
X = 140 - Y

Now you can go to the second equation...

X - Y = 12
And since we found out that X also = 140 - Y,
we can substitute 140 - Y for X in that equation, so

(140 - Y) - Y = 12
140 - 2Y = 12
- 2Y = - 128
and, Y = 64

If Y = 64, then we can find X...

Remember X - Y = 12,
So, X - 64 = 12
X = 76

2. ( X + 1.62 ) / 2 = 1.15m
X + 1.62 = 2.30m
X = 0.68 meters or 68 cm.

3. 12 Km trip...
2.60 + (11km x 0.10 x 5) = 2.60 + 5.50
= $ 8.10 total trip cost.

4. 78 + 78 + 10 + 10 = 176 meters perimeter of field.
176 meters x $ 25/meter cost = $ 4400 cost.

Have a Nice Day

-

Answer 3

You have two unknown numbers that you are trying to find. Since they are not known, represent them with variables.

Let X= larger number and Y = the smaller number.

You have two separate relationships between these two numbers. Translate each into an algebraic statement. The average (sum divided by two) is(=) 70. The difference (large number minus small number) is(=) 12.

(X+Y)/2=70
X-Y=12

You now have two equations with two variables. Solve using the substitutiion method or the addition method.

(X+Y)/2=70
X+Y=140 first equation
X-Y=12 second equation

2X=152 When added together, the Ys cancell out
x=76 The larger number is 76

The other number is 12 smaller, so it would be 64.

You'll find that the average of these two numbers is 70 and their difference is 12.

2. (fourboys + oneboy)/5=1.15 this is the average of the 5 boys.
oneboy is 1.62 m tall

(fourboys + 1.62)/5=1.15
fourboys + 1.62 = 5.75
fourboys = 4.13
fourboys/4 = 1.03 This is the average of four boys -- approximately 1.03 meters


3. 200 m = 0.2 km, 10 cents = $0.1
1st km of the 12 costs $2.60
The 11 other km cost $0,1 per 0.2 km
which is 11(0.1/0.2)
Total cost is 2.60 + 11(0.1/0.2)
2.60 + 11(1/2)
2.60 + 5.5
8.1
Total cost is $8.10


4.Total cost of fence equals number of meters times the cost for each meter. The total number of meters around a rectangular field is the definition of perimeter. Perimeter formula is:

P=2(L+W) where L = 12.78 m and W = 10 m
P=2(12.78 + 10)
P=2(22.78)
P=45.56m

It costs $25 for each meter of fence so:

Total cost is 45.56 m x $25/m
Total cost is $1139

Answer 4

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Answer 5

1) Total of the 2 numbers = 70x2 = 140
Smaller number = (140-12) / 2 = 64

2) Total Height of 5 boys = 1.15mx5 = 5.75m
Total Height of 4 boys = 5.75m-1.62m = 4.13m
Average Height of 4 boys = 4.13m/4 = 1.0325m

3) Total cost = $2.60 + [(12000m-1000m)/200m] x $0.10 = $8.10

4) Perimeter of rectangular field = (12.78m+10m)x2 = 45.56m
Cost of fencing = $25/m x 45.56m = $1,139

Answer 6

solving the first problem...
let numbers be ' x' and' y' so according to given condition...
x+y/2=70 or, x+y=140 ...(1)

and according to the given condition ...
x-y=12 ...(2)
or x=12+y ...(3)
subsitituting equation(3) in (1) we have ...
12+y+y=140 or,12+2y=140 or,6+y=70 or, y=70-6 or, y=64

as from equation (2) ...
x-y=12
so if y=4 than ...
x-64=12 or, x=76
RESULT: x=76 &y=64

Answer 7

Just a piece of advice: Don't fall into the trap
of thinking there is a formula for everything.
The purpose of these exercises is to teach
you how to set them up. Learn the METHOD
for doing so!

Answer 8

1.the equations are x+y=140
x-y=12
adding 2x=152 swo x=76
smaller no is 64
2.total of 5 boys=5.75
one boy's ht=1.62
total os remaining 4 boys=4.13
average of the remaining 4 boys=4.13/4=1.0325
3.fixed charge=$2.60
variable charge=(12000/200)*0.10=$6.00
total charges=$8.60
4.cost =perimeter*price
=2(12.78+10)25=50*22.78=$1139

Answer 9

1.the equations are x+y=140
x-y=12
adding 2x=152 swo x=76
smaller no is 64
2.total of 5 boys=5.75
one boy's ht=1.62
total os remaining 4 boys=4.13
average of the remaining 4 boys=4.13/4=1.0325
3.fixed charge=$2.60
variable charge=(12000/200)*0.10=$6.00
total charges=$8.60
4.cost =perimeter*price
=2(12.78+10)25=50*22.78=$1139

Answer 10

Why dint you give this problem as 4 separate problems? Fear of loosing 20 points?