Answer and Step-by-step explanation:
1. We see that we're adding single digits, but they need to create a two digit number. So, we must carry at least a 1.
H cannot be any number bigger than 2 because no three single digits can add up to a number with a tens digit greater than 2.
Let's try H = 1 and A equals any number greater than or equal to 5. We try a few, but see that none of them will work except when A = 9.
Thus, H = 1 and A = 9.
2. We see first off that the ones digit of Y * 3 must equal Y. So, looking through the digits 0 - 9, we see that Y can only be 0 or 5.
Now, let's look at SAY. We can write this in the form of 100*S + 10*A + Y. We are multiplying this by 3, so: 3 * (100*S + 10*A + Y) = 300S + 30A + Y.
Similarly, let's write BABY as 1000B + 100A + 10B + Y = 1010B + 100A + Y.
We set these two expressions equal to each other:
300S + 30A + Y = 1010B + 100A + Y
Simplifying and combining like terms, we see that:
300S = 1010B + 70A
Dividing both sides by 10:
30S = 101B + 7A
Now, we can start trying a few numbers. B cannot equal 0 because it's the leading number in BABY, so let's try B = 1. Then, we have:
30S = 101 + 7A
Now, in order for 101 + 7A to equal 30S, it must be a multiple of 30. The multiples of 30 between 100 and 200 are: 120, 150, and 180.
We can set each of these three numbers equal to 101 + 7A and see if we get an integer for A. We see that 150 works: 150 = 101 + 7A ⇒ A = 7
Then, A = 7, S = 5 (because 30 * 5 = 150), and B = 1. Y can either be 0 or 5; it doesn't matter unless the problem says that all the digits are different. If so, then Y = 0.
So: SAY = 570 and BABY = 1710.
Whew! Hope this helps!!
