Find two numbers if their sum is 91 and the ratio is 6:7.

Question

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Answer 1

Two numbers x and y have the ratio a:b if there is an number n such that a*n=x and b*n=y.

 

For this problem the ratio is 6:7.  There is a number n such that 6n=x and 7n=y.

 

Given, the sum of x+y = 91

                         (6n) + (7n) = 91

                            13n = 91

                                  n = 7

So,

     x = a*n = 6*7 = 42

     y = b*n = 7*7 = 49

 

Check:

  The ratio of 42:49 is 6:7.

  The sum 42+49 = 91

Answer 2

let x and y be the numbers

x+y=91

x/y=6/7

cross multiply

7x=6y

x=(6/7)y

substitute in the equation x+y=91

(6/7)y+y=91

(1 6/7)y=91

(13/7)y=91

multiply both sides by 7/13

(7/13)(13/7)y=(7/13)(91)

y=7*7 because when you simplify 13 goes into 91 7 times

y=49

x+49=91

x=91-49

x=42

42 and 49 are the numbers

42+49=91 and 42/49=6/7

you can also solve the problem like so:

x+y=91

y=91-x

x/(91-x)=6/7

7x=6(91-x)

7x=546-6x

7x+6x=546

13x=546

x=546/13

x=42 and y=91-42=49

however, the simplest thing to do is 6+7=13, 91/13=7, 7*6=42 and 7*7=49