Question

How do you solve `\frac { 2} { 5} ( 7+ \frac { 8} { p } ) + \frac { 3} { 10} ( 7+ \frac { 14} { p } ) = 100`?

Answer 1

`color(maroon)(p = 74 / 951`

Explanation:

`2/5(7 + 8/p) + 3/10 (7 + 14/p) = 100`

`14/5 + 16/(5p) + 21/10 + 42/(10p) = 100`, removing braces.

`(16/(5p) + 21/(5p)) + (14/5 + 21/10) = 100` bringing like terms together.

`37/(5p) + ((28+21)/10) = 100`

`37 / (5p) = 100 - 49/10 = 951/10`

`5p * 951 = 370`, cross multiplying.

`p = (370 / (5 * 951)) = 74/951`

Answer 2

`p = 74/951`

Explanation:

`2/5(7+8/p) +3/10(7+14/p)=100`

Multiply by the LCM of denominators to cancel the fractions.

`LCM = color(blue)(10p)`

`(color(blue)(cancel10^2p)xx2)/cancel5(7+8/p) +(color(blue)(cancel10p)xx3)/cancel10(7+14/p)=color(blue)(10p)xx100`

`28p +32 +21p+42 = 1000p`

`74 = 1000p -49p`

`74 = 951p`

`74/951 =p`