Lucy is thinking of a two digit number. The number is a multiple of five. When Lucy adds three to the number, it is divisible by seven. The number is greater than 40 but smaller than 90. find the value of half the number Lucy is thinking of.
The possible multiples of five between 40 and 90 are 45, 50, 55, 60, 65, 70, 75, 80, and 85.
Now, let's check which of these numbers, when added by 3, is divisible by 7:
45 + 3 = 48 (not divisible by 7)
50 + 3 = 53 (not divisible by 7)
55 + 3 = 58 (not divisible by 7)
60 + 3 = 63 (divisible by 7)
65 + 3 = 68 (not divisible by 7)
70 + 3 = 73 (not divisible by 7)
75 + 3 = 78 (divisible by 7)
80 + 3 = 83 (not divisible by 7)
85 + 3 = 88 (not divisible by 7)
Therefore, the two-digit number Lucy is thinking of is 75. Half of 75 is 37.5.