Question

Find 2 numbers that the sum of 1/3 of the first plus 1/5 of the second will be equal to 13 and that if you multiply the first by 5 and the second by 7 you get 247 as the sum of the two products with replacement solution

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Miles

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Let's set up a system of equations to find the two numbers. Let the first number be "x," and the second number be "y."
From the first statement, we have:
(1/3)x + (1/5)y = 13
From the second statement, we have:
5x + 7y = 247
Now, we can solve this system of equations. First, we can eliminate fractions by multiplying both sides of the first equation by the least common multiple (LCM) of 3 and 5, which is 15:
(15 * (1/3))x + (15 * (1/5))y = 15 * 13
5x + 3y = 195
Now, we have the system of equations:
5x + 3y = 195
5x + 7y = 247
Subtract the first equation from the second equation to eliminate "x":
(5x + 7y) - (5x + 3y) = 247 - 195
(5x - 5x) + (7y - 3y) = 52
4y = 52
Now, solve for "y":
y = 52 / 4
y = 13
Now that we have the value of "y," we can substitute it back into one of the original equations. Let's use the second equation:
5x + 7y = 247
5x + 7(13) = 247
5x + 91 = 247
Subtract 91 from both sides:
5x = 247 - 91
5x = 156
Now, solve for "x":
x = 156 / 5
x = 31.2
So, the two numbers that satisfy the conditions are x = 31.2 and y = 13.

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