LOL I can't figure this out. It should be easy it's been years since I've been in school and my son has no idea.
The product of two numbers is 63. Their sum is 16. What are the numbers?
Thanks for the help!
Let's factor 63.
1 x 63; 3 x 21; 7 x 9.
Which of those pairs of numbers adds up to 16?
If you want to do this all math, with no reasoning.
eqn 1:     xy = 63
eqn 2:     x+y=16
Solve for x and y.
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solve for x from eqn 1.
x = 63/y
Plug this value into eqn 2 for x.
(63/y)+y=16
Multiply through by y
63 + y^2 = 16y
Rearrange
y^2 - 16y + 63 = 0
factor
(y-9)(y-7)=0
y=9 or 7
If y = 9, then
x=63/9=7 and the reverse is true.
So, y=9 and x=7 OR
y=7 and x=9
See, I didn't say this was an easier way to do it. It's an all math way of doing it. Reasoning it out is far simpler.
Good luck helping your son.
I THINK IT'S 7x9!
Yes, you are correct! The two numbers that have a product of 63 and a sum of 16 are 7 and 9. Well done!
To find the numbers, you can factorize 63 into its prime factors, which are 7 and 9. Then, check which pair of factors satisfies the second condition, which is that their sum is 16. In this case, 7 + 9 equals 16, so 7 and 9 are the correct pair of numbers.
Alternatively, you can solve the problem algebraically by setting up two equations:
Let x be one of the numbers, and let y be the other number.
From the given information, we can set up two equations:
1. xy = 63 (the product of the two numbers is 63).
2. x + y = 16 (the sum of the two numbers is 16).
By rearranging equation 2, we can express one variable in terms of the other:
x = 16 - y
Substitute this value of x into equation 1:
(16 - y)y = 63
Rearrange the equation:
y^2 - 16y + 63 = 0
Factorize the left side:
(y - 7)(y - 9) = 0
From this equation, we find two possible values for y:
y - 7 = 0 (which gives y = 7)
or
y - 9 = 0 (which gives y = 9)
Substitute these values of y back into equation 2 to find the corresponding values of x:
For y = 7, x = 16 - 7 = 9.
For y = 9, x = 16 - 9 = 7.
So, the two numbers are 7 and 9, which confirms your answer. Keep up the good work!