Tom and Dan were given some sweets. At first, Tom took 8/9 of the sweets. When he gave Dan 42 sweets, the number of sweets they had became equal. How many sweets were they given in all?
sorry i don't know how to do LaTeX
First, I will multiply the top and bottom of the fraction 8/9 so the bottom is even.
If Tom originally had 8/9 of the sweets and gave away 42 to make it equal, that shows that 42 sweets is exactly 7/18 of the total. We can then create the equation with x being the total sweets they were given:
x * 7/18 = 42
dividing each side by 7, we get
x/18 = 6
so we can multiply each side by 18 to get
x = 108