Question

Ten times a number r plus one-fifth of a number s equals sixteen. Five times the number r plus one-tenth of the number s equals five. What are the two numbers?

Answer 1

Explanation:

10r + s/5 = 16

5r + s/10 = 5

Use simulataneous equations to cancel out one of the 2 unknowns

10r + s/5 = 16

10r + s/5

wait this wont work, i think there is something wrong with the questions

Answer 2

Explanation:

Let's call the first number "r" and the second number "s". We can set up two equations based on the information given:

10r + (1/5)s = 16 (equation 1)

5r + (1/10)s = 5 (equation 2)

We can use the second equation to solve for one of the variables in terms of the other.

5r + (1/10)s = 5

Subtract (1/10)s from both sides:

5r = 5 - (1/10)s

Divide both sides by 5:

r = 1 - (1/50)s

Now we can substitute this expression for r into the first equation:

10r + (1/5)s = 16

10(1 - (1/50)s) + (1/5)s = 16

Expand:

10 - (1/5)s + (1/5)s = 16

Combine like terms:

10 = 16

This is a contradiction, so there are no values of r and s that satisfy both equations. Therefore, there is no solution to this system of equations.