21. The difference between two numbers is 29. If five times the smaller is subtracted from twice the larger, the result will be one. What is the larger number?

48

Step-by-step explanation:

We have to write a system of equations:

The difference between two numbers is 29. Difference means one number (y) minus another number (x) equals 29.

y-x =29

If five times the smaller ( 5 times x , x is the smaller number because is the number to subtract) is subtracted from twice the larger, (2y)

The result will be one

2y-5x =1

Now, we have to multiply the first equation by 2, and subtract the second equation to the first one:

2y -2x = 58

-

2y-5x =1

3x =57

Solve for x:

x =57/3 =19

Replacing the value of x on any equation:

y-x =29

y-19 =29

y = 29+19 = 48

48 (y)> 19(x)

Feel free to ask for more if needed or if you did not understand something.  

answer: the common difference is -0.10

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step-by-step explanation: