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

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Answer 1 · 2018-07-29T14:57:36

$p = \frac{74}{951}$ $color(maroon)(p = 74 / 951$

$\frac{2}{5} (7 + \frac{8}{p}) + \frac{3}{10} (7 + \frac{14}{p}) = 100$ $2/5(7 + 8/p) + 3/10 (7 + 14/p) = 100$

$\frac{14}{5} + \frac{16}{5 p} + \frac{21}{10} + \frac{42}{10 p} = 100$ $14/5 + 16/(5p) + 21/10 + 42/(10p) = 100$ , removing braces.

$(\frac{16}{5 p} + \frac{21}{5 p}) + (\frac{14}{5} + \frac{21}{10}) = 100$ $(16/(5p) + 21/(5p)) + (14/5 + 21/10) = 100$ bringing like terms together.

$\frac{37}{5 p} + (\frac{28 + 21}{10}) = 100$ $37/(5p) + ((28+21)/10) = 100$

$\frac{37}{5 p} = 100 - \frac{49}{10} = \frac{951}{10}$ $37 / (5p) = 100 - 49/10 = 951/10$

$5 p \cdot 951 = 370$ $5p * 951 = 370$ , cross multiplying.

$p = (\frac{370}{5 \cdot 951}) = \frac{74}{951}$ $p = (370 / (5 * 951)) = 74/951$

Answer 2 · 2018-07-29T15:13:31

$p = \frac{74}{951}$ $p = 74/951$

$\frac{2}{5} (7 + \frac{8}{p}) + \frac{3}{10} (7 + \frac{14}{p}) = 100$ $2/5(7+8/p) +3/10(7+14/p)=100$

Multiply by the LCM of denominators to cancel the fractions.

$L C M = 10 p$ $LCM = color(blue)(10p)$

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

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

$74 = 1000p -49p$

$74 = 951p$

$74/951 =p$

How do you solve \frac { 2} { 5} ( 7+ \frac { 8} { p } ) + \frac { 3} { 10} ( 7+ \frac { 14} { p } ) = 10025(7+8p)+310(7+14p)=100\frac { 2} { 5} ( 7+ \frac { 8} { p } ) + \frac { 3} { 10} ( 7+ \frac { 14} { p } ) = 100?