13. A number is 7 more than another number. The sum of the numbers is 15. Find the numbers. 14. One number is two times the other, and their sum is 27. What are the numbers? 15. Thirteen is the sum of two numbers and their difference is equal to five. Find the numbers

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mireyagonz2022 mireyagonz2022

30-04-2024
Mathematics

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13. A number is 7 more than another number. The sum of the numbers is 15. Find the numbers. 14. One number is two times the other, and their sum is 27. What are the numbers? 15. Thirteen is the sum of two numbers and their difference is equal to five. Find the numbers

Answer :

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sqdancefan sqdancefan · Answer 1 · 2024-04-30T16:23:45-04:00

Answer:

13. 11 and 4

14. 18 and 9

15. 9 and 4

Step-by-step explanation:

You want the pairs of numbers that satisfy different relations:

13. sum of 15, difference of 7
14. ratio of 2:1, total of 27
15. sum of 13, difference of 5

Sum and difference

Consider the sum and difference problem:

a + b = s . . . . . sum

a - b = d . . . . . difference

Adding these two equations gives ...

(a +b) +(a -b) = (s) +(d)

2a = s +d

a = (s +d)/2

Using the second equation to find b, we have ...

b = a -d

13. (S, D) = (15, 7)

The two numbers are ...

(15 +7)/2 = 11

11 -7 = 4

15. (S, D) = (13, 5)

The two numbers are ...

(13 +5)/2 = 9

9 -5 = 4

14. Ratio

When two numbers that total N have the ratio a : b, the first of them is ...

a/(a+b) · N

and the second of them is ...

b/(a+b) · N . . . . . . . also equal to N-a

The problem asks for two numbers that total 27 and have the ratio 2:1.

The larger is 2/(2+1)·27 = 18.

The smaller is 1/(2+1) ·27 = 9.