The sum of two numbers is 25. One of the numbers exceeds the other by 9. Find the numbers.

The sum of two consecutive multiples of 5 is 55. Find these multiples.

If 3/5th of a number is 4 more than 1/2 the number, then what is the number?

When 142 is added to a number, the result is 64 more than 3 times the number. Find the number.

The sum of three consecutive numbers is 243. Find the numbers.

The denominator of a fraction is greater than its numerator by 3. If the numerator is increased by 7 and the denominator is decreased by 1, the new number becomes 3/2. Find the original number.

The sum of the digits of a two digit number is 7. If the number formed by reversing the digits is less than the original number by 27, find the original number.

The units digit in a two-digit number is one more than twice the ten's digit. Find the number if the sum of the digit is 7.

The sum of three consecutive multiples of 4 is 444. Find these three consecutive multiples of 4.

With solutions thanks!

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Answers

2014-09-30T19:48:59+08:00
a.       Let x and x+9 so... à x+x+9=25 à 2x+9=25 à 2x=25-9 à 2x/2=16/2 à x=8  

b.     
Let x be one of the number and x+5 for the other since it’s a multiple of 5 so...
x+x+5=55 à 2x/2=55/2 à x=27.5 since it’s a consecutive multiple the two numbers are 27 and 28.  

c.      
3/5th of a number is 4 more than 1/2 the number the equation is à 3/5x = 4+1/2x à 10[3/5x = 4+1/2x] à 6x = 40+5x à 6x-5x = 40 à x = 40
 

d.     
When 142 is added to a number, the result is 64 more than 3 times the number the equation is à 142+x = 64+3x à 142-64 = 3x-x à 2x/2 = 78/2 à x = 9
                                      
e.       We assume that the three consecutive numbers are x, x+1 and x+2 so... x+x+1+x+2 = 243 à 3x+3 = 243 à 3x = 243-3 à 3x/3 = 240/3 à x = 80, x+1 à 80+1 à81 and x+2 à 80+2 à 82 so the numbers are 80, 81 and 82  

f.      
Let x be the numerator so...  =  à 2[(x+3)-1] [ =  à 2x+14 = 3x+9-3 à2x+14 = 3x+6 à 3x-2x = 14-6 à x = 8
 

g.     
Trial and Error 52 and 25 are the answers.
 

h.     
Let the one’s be 2x+1 and the ten’s be x so... x+2x+1 = 7 à 3x+1 = 7 à 3x = 7-1 à 3x/3 = 6/3 à x = 2 so the tens is 2 and the ones is 2x+1 à 2(2)+1 à 5 so the digit is 25
   

i.       
We assume that the three consecutive numbers are x, x+4 and x+8 so... x+x+4+x+8 = 444 à 3x+12 = 444 à 3x = 144-12 à3x/3 = 132/3 àx = 44, x+4 à 44+4 à48 and x+8 à 44+8 à 52 so the numbers are 44, 48 and 52
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