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1. The sum of two numbers is . The difference of the same two numbers is . What are the two numbers? 2. Grace is older than Paolo. Three years ago, she was twice as old as Paolo. How old are they now?
The Sum of Two Numbers is 15 and Their Difference is 7
x + y = 15
The difference between x and y is 7. In other words, x minus y equals 7 and can be written as equation B:x - y = 7
Now solve equation B for x to get the revised equation B: x - y = 7
x = 7 + y
x + y = 15
7 + y + y = 15
7 + 2y = 15
2y = 8
y = 4
Now we know y is 4. Which means that we can substitute y for 4 in equation A and solve for x: x + y = 15
x + 4 = 15
X = 11
Sum: 11 + 4 = 15
Difference: 11 - 4 = 7
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The Sum of Two Numbers is 15 and Their Difference is 8
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2 Answers By Expert Tutors
Oluwadamilola F. answered • 03/02/20
Skilled and Experienced Math and Science Tutor
Let the numbers be x and y
X + Y =15
X -Y = 7
Make X subject of formula in equation 1
X = 15-Y
Substitute for X in equation 2
15 -Y -Y = 7
15 - 2Y = 7
15 - 7 = 2Y
8 = 2Y
Divide both sides by 2
Y = 4
Substitute for Y in equation 3
X=15 -Y
X=15-4
X=11
Therefore the numbers are 11 and 4
Christina B. answered • 03/02/20
Experienced, Positive, and Effective Tutor with an M.Ed.
Hi Kimberly,
One way to solve this problem is to reason about the possible answers:
"The sum of two numbers is 15"
We can list the possible numbers that combine to form a sum of 15.
1+14
2+13
3+12
4+11
5+10
6+9
7+8
It is also possible that one of the numbers is negative.
16+-1
17+-2
18+-3
19+-4
20+-5
21+-6
22+-7
This list is infinite, as we can simply keep counting up.
"And the difference is 7."
In the above lists, are there any pairs of numbers that, if you were to subtract one from other other, their difference is 7? I see one pair in the list of positive numbers where the difference is 7.
In the list of positive numbers paired with negative numbers, the differences start at 17 and grow from there. So there are no possible answers on that list.
I hope that helps! If this answer was helpful, please upvote it.