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The sum of two numbers is 19. The sum of twice the smaller number and thrice the larger number is 48. What are the two numbers?

Sagot :

Alphabetagammaid
Let x be the smaller number and be the larger number. Then,
x + y = 19
2x + 3y = 48

First equation can be transformed as x = 19 - y.

Substituting this value to the second equation, we have
2(19 - y) + 3y = 48
38 - 2y + 3y = 48
38 + y = 48
y = 48 - 38
y = 10

Substituting the value of y to either of the two equations, we have
x + y = 19
x + 10 = 19
x = 19 - 10
x = 9

The two numbers are 9 and 10.

- D.E.


AwesomeHelperid
Let x be the first number. It is the smaller number.
Let y be the second number. It is the larger number.

x + y = 19
2x + 3y = 48

Using Gaussian Elimination Method:
[tex] \left[\begin{array}{ccc}1&1&19\\2&3&48\\\end{array}\right] R1(2) - R2 = R2 \left[\begin{array}{ccc}1&1&19\\0&-1&-10\\\end{array}\right] R2(-1) \left[\begin{array}{ccc}1&1&19\\0&1&10\\\end{array}\right] \\ R1 - R2 = R1 \left[\begin{array}{ccc}1&0&9\\0&1&10\\\end{array}\right] [/tex]

So therefore, the numbers are 9 and 10.

Check:
9 + 10 = 19
2(9) + 3(10) = 48
18 + 30 = 48
48 = 48