Solve the mathematical puzzle.
Determine the digits of R from these clues.
The first digit is the answer when the third digit is divided by 2.
The second and third digits add to 7.
The second digit minus the first digit is 1.
R is a three-digit number: ____
I have never understood how to do this.
Call the digits a,b,c left-to-right
a = c/2
b+c = 7
b-a = 1
we see that c=2a, so
b+2a=7
b-a=1
subtract to get
3a=6
a=2
Thus c=4 and b=3
R=234
Or, just working with the specs,
c must be even, since it can be divided by 2. So, R is one of the forms
1x2
2x4
3x6
4x8
Since the last two add to 7, R must be
152
234
316
Since 2nd-1st=1,
R=234
To solve this mathematical puzzle, we will follow a step-by-step approach. Let's break down the information given:
1. "The first digit is the answer when the third digit is divided by 2."
Let's represent the first digit as A, the second digit as B, and the third digit as C. According to the clue, A = C/2.
2. "The second and third digits add to 7."
This means that B + C = 7.
3. "The second digit minus the first digit is 1."
This clue tells us that B - A = 1.
Now, we can use these equations to solve for the values of A, B, and C.
From clue 1: A = C/2. Since A is a digit, we know that C must be even (as dividing an odd number by 2 will not yield an integer). We can start by assuming the possible values for C (2, 4, 6, or 8) and calculate the corresponding values of A using the equation A = C/2.
Let's go through the possibilities:
1. If C = 2, then A = 2/2 = 1. This would imply the second digit is 1 (B = A + 1 = 1 + 1 = 2), which contradicts clue 2 (B + C = 7), as 2 + 2 = 4.
Now, let's move on to the next possibility:
2. If C = 4, then A = 4/2 = 2. This satisfies clue 1. For the second digit, we know that B - A = 1, so B = A + 1 = 2 + 1 = 3. This also satisfies clue 2 (B + C = 3 + 4 = 7). Therefore, A = 2, B = 3, and C = 4.
So, the three-digit number R is 234.
No problem, I can help you solve this mathematical puzzle step-by-step.
Let's assume the three-digit number R is represented by ABC, where A is the first digit, B is the second digit, and C is the third digit.
From the first clue, we know that A is the answer when C is divided by 2. So, if we divide C by 2, it equals A.
From the second clue, we know that B + C = 7.
From the third clue, we know that B - A = 1.
Let's use these clues to solve for the digits of R:
1. From the first clue, we have C/2 = A. Multiplying both sides of the equation by 2 gives us C = 2A.
2. Using the information from the third clue, we have B - A = 1. Adding A to both sides of this equation gives us B = A + 1.
3. Now, substitute the value of B from equation 2 into equation 1. We get C = 2A.
4. Substitute the value of B from equation 2 into equation 2. We get A + A + 1 = 7. Simplifying this equation gives us 2A + 1 = 7.
5. Subtract 1 from both sides of equation 4 to get 2A = 6.
6. Divide both sides of equation 5 by 2 to get A = 3.
7. Now that we know A = 3, we can substitute this value into equation 2 to find B. B = 3 + 1, so B = 4.
8. Finally, substitute the values of A = 3 and B = 4 into equation 1 to find C. C = 2 * 3, so C = 6.
Therefore, the three-digit number R is 346.