what are two whole numbers whose product is 1224 and whose sum is 70
Unless I am mistaken, the two numbers you are looking for are 36 and 34.
34 x 36 = 1224
34 + 36 = 70
Let x = first number
Let y = second number
x * y = 1224
x + y = 70
Express y in terms of x to eliminate 1 variable:
y=1224/x
The second equation can be written as
x + (1224/x) = 70
Multiply both sides by x
x^2 + 1224 = 70x
subtrace 70x from both sides
x^2 - 70x + 1224 = 0
Factor or solve the quadratic.
To find two whole numbers whose product is 1224 and whose sum is 70, we can use a systematic approach by checking all possible pairs of numbers until we find the correct solution.
Let's start by listing all the whole numbers that can possibly be one of the numbers (let's call it x). Since the product of the two numbers is 1224, and we are looking for whole numbers, x must be a factor of 1224.
Factors of 1224:
1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 204, 306, 408, 612, 1224
Now, we will go through each factor of 1224 and look for the other number (let's call it y) such that x*y = 1224 and x+y = 70.
1. If x = 1, then y = 1224/1 = 1224. But 1 + 1224 ≠ 70, so this is not a solution.
2. If x = 2, then y = 1224/2 = 612. But 2 + 612 ≠ 70, so this is not a solution.
3. If x = 3, then y = 1224/3 = 408. But 3 + 408 ≠ 70, so this is not a solution.
4. If x = 4, then y = 1224/4 = 306. But 4 + 306 ≠ 70, so this is not a solution.
5. If x = 6, then y = 1224/6 = 204. But 6 + 204 ≠ 70, so this is not a solution.
6. If x = 8, then y = 1224/8 = 153. But 8 + 153 ≠ 70, so this is not a solution.
7. If x = 9, then y = 1224/9 = 136. And 9 + 136 = 70, so this is a solution. The two numbers are 9 and 136.
Therefore, the two whole numbers whose product is 1224 and whose sum is 70 are 9 and 136.
To find two whole numbers whose product is 1224 and whose sum is 70, you can use a systematic approach called factorization.
Step 1: Begin by finding the factors of 1224. Factors are the numbers that can be multiplied together to get a given product.
Factors of 1224: 1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 102, 136, 204, 306, 408, 612, 1224
Step 2: Now, look for two factors that add up to 70. Start with the highest factor and work your way down.
The factors of 1224 that add up to 70 are 51 and 19.
So, the two whole numbers are 51 and 19.