Help with problem 1 and 2

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!!

1) A = 9, H = 1

2) SAY: 570

BABY: 1710

Step-by-step explanation:

A + A + H = 10H + A

A = 9H

Only possible combination is:

A = 9, H = 1

(100S + 10A + Y) × 3 = 1000B + 100A + 10B + Y

300S + 30A + 3Y = 1010B + 100A + Y

300S + 2Y = 1010B + 70A

Y is a multiple of 3: 0,3, 6, 9

S》3

B can be 1 or 2

2B + A + Y is a multiple of 3

300S + 2Y = 1010B + 70A

Since other 3 terms are a multiple of 10, 2Y has to be too.

That's only possible when Y = 0

(Because is has to be a multiple of 3 as well)

300S = 1010B + 70A

30S = 101B + 7A

S》3

B can be 1 or 2

2B + A is a multiple of 3

30() = 101(2) + 7(7)

150 = 101 + 49

S = 5, B = 1, A = 7

Y = 0

SAY: 570

BABY: 1710