Digit Problems Alg. 1

Question

equation 1- the sum of the digits of the reverse of the original number, multiplied by two is 20. equation 2- four times the tens digit in the original number equals the units digit.

Answer 1

This looks really complicated, but it is simpler than it looks :)

Let's start with an example number, for instance, 35. 3 would be the first, or the TENS digit, and the 5 would be the second, or the UNITS digit.

Now let's have T represent the TENS digit, and U represent the UNITS digit, and then recreate the equations by substituting these symbols in.

Equation 1: The sum of the digits of the reverse of the original number x2 equals 20.

1. Ignore the 'reverse' part - that is just there to confuse you. The sum of the digits will be the same either way! We can rewrite this equation as (U + T) x 2 = 20

Equation 2: 4 times the 10s digit in the original number equals the units digit.

1. We can rewrite this equation as 4 x T = U

Now we combine the equations. Equation 2 shows that U = 4T, so we can substitute this value of U into the first equation, as shown below:

1. (4T + T) x 2 = 20

Equation 1 can now be simplified to 5T x 2 = 20, or 10T = 20, and we can solve for T to show that T = 2.

Now we substitute T = 2 back into Equation 2, and we see that U = 4 x 2, or U = 8.

Put the Tens digit and the Units digit together, and you have 28 as the original number!

You can then check the work and see if 28 fits both Equations 1 and 2.