Final answer:
Using system of equations to find two numbers whose sum is 117 and whose scaled sum is 623 results in the numbers being 68 and 49, which does not match any of the provided multiple-choice answers.
Step-by-step explanation:
To solve for the two numbers based on the given conditions, we can set up a system of linear equations. Let's call the first number x and the second number y. The first equation, based on the sum of the numbers, is x + y = 117. The second equation, based on the combination of seven times one number and three times the other, is 7x + 3y = 623.
Solving the first equation for y, we get y = 117 - x. We can substitute this into the second equation to find x:
7x + 3(117 - x) = 623
7x + 351 - 3x = 623
4x = 272
x = 68
Now we can substitute x = 68 back into the first equation to find y:
y = 117 - 68
y = 49
The two numbers are 68 and 49. However, none of the provided options (a) 47 and 70, (b) 30 and 87, (c) 50 and 67, (d) 60 and 57 exactly match these results, so there could be a typo or an error in the options given.