solve a problem involving products, quotients and sums

[skhan]

Ali and April each think of a different 2 digit number between 10 and 60. Ali multiply his number by 7 and then subtract 42 . April divide her number by 8 and add 42. they both got the same answer. what is the sum of their original number.

 

[Deleted member 4993]

Ali and April each think of a different 2 digit number between 10 and 60. Ali multiply his number by 7 and then subtract 42 . April divide her number by 8 and add 42. they both got the same answer. what is the sum of their original number.

Please follow our rules regarding post - enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-459460

Hint:

1) Name the variables

Ali's number = L

April's number =R

You need to find......... L+R

Continue,,,,,,,

 

[HallsofIvy]

"Ali and April each think of a different 2 digit number between 10 and 60."
Call Ali's number "L" and April's number R.

"Ali multiply his number by 7 and then subtract 42."
So 7L- 42

"April divide her number by 8 and add 42."
So 8R+ 42

"They both got the same answer."
7L- 42= 8R+ 42

"What is the sum of their original number?"
7L- 8R= 84

There exist an infinite number of "L, R" pairs that satisfy that.

 

[Deleted member 4993]

"Ali and April each think of a different 2 digit number between 10 and 60."
Call Ali's number "L" and April's number R.

"Ali multiply his number by 7 and then subtract 42."
So 7L- 42

"April divide her number by 8 and add 42."
So 8R+ 42

"They both got the same answer."
7L- 42= 8R+ 42

"What is the sum of their original number?"
7L- 8R= 84

There exist an infinite number of "L, R" pairs that satisfy that.

Since L and R are two digit numbers, bounded by 10 and 60, there are finite number of solutions. One of those solutions is (28, 14). We can add 8 and 7 to calculate the rest.

 

[HallsofIvy]

Yes, thanks. I forgot the "between 10 and 60" part!

 

[skhan]

"April divide her number by 8 and add 42."
So 8R+ 42........................WHY multiply. ? it says divide her number by 8?

Is not it R/8 + 42 ? but then what are the solutions ?

 

[Deleted member 4993]

Ali and April each think of a different 2 digit number between 10 and 60. Ali multiply his number by 7 and then subtract 42 . April divide her number by 8 and add 42. they both got the same answer. what is the sum of their original number.

You are correct. The equation should be:
7 * L - 42 = R/8 + 42

56 * L - R - 672 = 0

R = 672 - 56*L

Now there is only one solution within the domain.