A man buys some shirts and some ties. The shirts cost $7 each and the

Solution

• A man buys some shirts and some ties.
• Shirts cost $7 each and ties cost $3 each.

• The ratio of shirts to ties if the man buys maximum number of shirts possible and spends $81.

Let the man buys x shirts and y ties then the total spending by the man = 7x + 3y
• So, 7x + 3y = 81

o Now, if x is maximum then y has to be minimum.

• 7x = 81-3y

o So, 81- 3y must be a multiple of 7 and y will be minimum.
o For y= 1, 81-3y = 78 -> not a multiple of 7
o For y= 2, 81-6 = 75 -> not a multiple of 7
o For y= 3, 81-9 = 72 -> not a multiple of 7
o For y= 4, 81-12 = 69 -> not a multiple of 7
o For y= 5, 81-15 = 66 -> not a multiple of 7
o For y= 6, 81-18 = 63 -> A multiple of 7
• x = 9 and y=6
• x: y = 3: 2