Question

The cost of 8 hats and 5 scarves is the same as the cost of 5 hats and 7 scarves. The cost of each scarf is d times the cost of each hat. What is the value of d?

Answer 1

Let x = the cost of one hat, then dx = the cost of one scarf. Set the two instances equal to one another\[8x+5dx = 5x +7dx\]Get rid of the factor of x\[8+5d=5+7d\]\[2d=3\]\[d={3\over 2}\]