Question

How do you solve `\frac { 13} { 4} ( \frac { 31} { 8} r + 1) = \frac { 5423} { 56}`?

Answer 1

`r=7.43`

Explanation:

`13/4(31/8r+1)=5423/56`

As always, equations of one unknown can be approached by expanding, and then isolating the unknown one side of the equation.

`13/4*31/8r+13/4=5423/56`
`(13*31)/(4*8)r+13/4=5423/56`

Now we subtract `13/4` from both sides to get isolate the unknown's term. (The unknown's (r's) coefficient is also simplified.)

`403/32r+13/4-13/4=5423/56-13/4`
`403/32r=5423/56-13/4`

Then taking common denominator and simplifying the ride side of the equation.

`403/32r=5423/56-(13*14)/(4*14)` (since 4*14=56)
`403/32r=(5423-(13*14))/56`
`403/32r=(5423-182)/56` (since 13*14=182)
`403/32r=5241/56`

Now as of a final step we have to multiply both sides by 32 and divide by 403, to isolate the unknown.

`403/32r*32/403=5241/56*32/403`
`r=5241/56*32/403=(167712)/(22568)=7.43`
(since `5241*32=167712` and `56*403=22568`)

I hope that this helps. :)