One positive number is 5 times another number. The difference between the two numbers is 1352, find the numbers

1) y=5x
2) y-x=1352


then we can write

5x-x=1352
4x=1352
x=1352/4
x=338

so y=5(338)=1690

The sum of two numbers is 41, and their difference is 11. What are the two numbers?

1) n+m=14
2) n-m=11
adding 1) and 2)...
2n=25
n=25/2

m=14-25/2=3/2

A cup of skim milk has 10 more than half the calories of a cup of whole milk. a cup of whole milk has 40 more calories than a glass of apple juice. If someone consumed a cup of each of the three, they would have 370 calories. how many calories must be in each?

1) s= w/2+10
2) w=a+40 (or a=w-40)
3) a+s+w=370

rewriting 3)...






then we find the others:

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A number is divided by three. The result is divided by seven, for a final result of eight. What was the original number?

 


 

what multiplies to get -270 and adds to get -3?

1)xy=-270
2)x+y=-3


y=-x-3
x(-x-3)=-270
x^2+3x-270=0
(x-15)(x+18)=0

so, 15 and -18

Father is four times as old as his son today. Six years ago,the product of the number denoting their ages was 252. Find their present ages.

1) F=4x
2) (F-6)(x-6)=252

combining by substitution...
(4x-6)(x-6)=252
which has a solution of x=12 (the other is -9/2 and is extraneous for our goal)
so the father is 48 and the son is 12

if 1/2 of an integer is added to 1/4 to the next consecutive integer the sum is 22.find the integer.

multiplying by 4...

One number is 5 greater than another number. their sum is equal to 5 times their difference. Find the numbers.

1)x=y+5
2)x+y=5(x-y)

1) tells us x-y=5
therefore we can repalce x-y with 5 in 2)

new system:

x+y=25
x-y=5 

adding the two equations...

2x=30

x=15
so...

y=10

If the length is 3 cm and the perimeter is 10 cm, what will the width and area be? You can put this solution on YOUR website!

 

A rope 60 cm long is made to form a rectangle. if the length is four times its breath, calculate the length and diagonal of the rectangle.

which leads to

One sixth of the smallest of three consecutive even integers is three less than than one tenth the sum of the other two even integers. Find the integers.

n/6=((n+2) + (n+4))/10 - 3
n/6=(2n+6)/10-3
n/6=n/5+3/5-3
3-3/5=n/5-n/6
12/5=n/30

n=6*12=72

They are:
{72, 74, 76}

Kate is three times as old as her son. If Kate is 30 years older than her son, what are their ages?

Equations:

1) 3S=K
2) K=S+30

so
3S=S+30
2S=30
S=15

and so
K=45

The average of 9 consecutive numbers is 20 the greatest of these numbers is ?

x+(x+1)+...+(x+8)=9x+36

so if they average to 20 we can say:

(9x+36)/9=20

simplifying...

x+4=20,

so x=16

the greatest of the 9 numbers must be 24

Find the value of X and Y from the given equation : sqrt(X)+Y=7 & sqrt(Y)+X=11

Usually these types of problems can be very challenging. But no need to do any "real" work for this problem since the numbers a so easy to work with. Clearly x and y have to be 9 and 4 (why?) So we'll just check them...
3+4=7 so far so good...
2+9=11...perfect
x=9, y=4

A boat can go 72 miles downstream in 3 hours, and can make the return trip in 4 hours. Find the speed of the boat in still water.

up: (s+c)3=72, 
down: (s-c)4=72 

adding... 
2s=72(1/3+1/4) 

then... 
s=21 
boat speed: 21mph

The product of two numbers is less than 340. One of the number is 3 less than the other , what are the possible values of the number?

We are looking for divisors of 340 that differ by 3. The only two are 17 and 20.

Parking garage charges $1.00 for first half hour and $0.60 for each additional half hour. Write an equation and solve to find how long you can park with $6.00.

c(t)=1.00+0.60t   if t>1 hr

For c(t)=$6.00 we get:

6=1+.6t
5=.6t
t=5/0.6

t=8 1/3 hours (8 hrs 20 min)

Aman left 1/3rd of his money to his daughter,1/4th to his son , and the remaining 20,000 to his wife. How much money did the man have?

1/3+1/4=

7/12 

so T- 7/12 T =20000
5/12T=20000
T=48000

Four times a number, diminished by 6, yields the same result as twice the same number increased by 4. Find the number.

4x-6=2x+4
4x-2x=4+6
2x=10
x=5

Kayla has 80 coins in her bank. They are all dimes and nickels. She ha four times as many dimes as nickels. How much money does she have in her bank?

x+4x=80

5x=80

x=16

so she has 16 nickels (and so 64 dimes)

therefore she has 64*0.1+16*0.05 i.e. $7.20