help

Sarah and Henry share some sweets in the ratio 7:6 .
Sarah eats 24 of her sweets and the ratio of sweets left becomes 1:2 .
How many sweets did Henry have?

Hello Guest!

\(6s=7h\\ s=\frac{7h}{6}\\ (s-24):h=1:2\\ (\frac{7h}{6}-24):h=1:2\\ \frac{7h}{3}-48=h\)

\(\frac{7h}{3}-\frac{3h}{3}=48\\ \frac{4h}{3}=48\)

\(h=36\)

Henry had and still has 36 sweets.

  !
 

s/h = 7/6       or   s = 7/6 h

then

(s-24) / h = 1/2

     or     s = 1/2 h +24      equate to the red equation:

                                              7/6 h = 1/2 h + 24

                                               4/6 h = 24

                                                      h = 24 * 6/4 = 36