Rasheed bought two kinds of candy bars, chocolate and toffee, that came in packages of 2 bars each. He handed out rac{2}{3} of the chocolate bars and rac{3}{5} of the toffee bars. How many packages of chocolate bars did Rasheed buy?

Mathematics, 13.03.2020 21:39 kyleee4473

Rasheed bought two kinds of candy bars, chocolate and toffee, that came in packages of 2 bars each. He handed out \frac{2}{3} of the chocolate bars and \frac{3}{5} of the toffee bars. How many packages of chocolate bars did Rasheed buy?

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Answer from: lovvyDovvy04

Rasheed bought 9 packages of chocolate bars

Step-by-step explanation:

Rasheed bought two kinds of candy bars, chocolate and toffee, that came in packages of 2 bars each.

Let 'cb' represent the number of chocolate bars that Rasheed bought

Let 'tb' represent the number of toffee bars that Rasheed bought

If Rasheed bought 1 fewer package of chocolate bars than toffee bars; we have the following suitable expression

cb = tb - 1

Also; he handed out $\frac{2}{3}$ of the cb and $\frac{3}{5}$ of tb; we have:

$\frac{2}{3} *cb = \frac{3}{5}*tb$

10cb = 9tb

If we make tb the subject of the formula since we are only looking for the number of chocolate bars Rasheed bought; we have:

$tb=\frac{10}{9} cb$

From the previous expression cb = tb - 1

1 = tb - cb

Replacing $tb=\frac{10}{9} cb$ in the above equation; we have:

$1= \frac{10cb}{9} -\frac{cb }{1}$

$1 = \frac{1cb-9cb}{9}$

$1 = \frac{1cb}{9}$

cb = 1*9

cb = 9

Hence,Rasheed bought 9 packages of chocolate bars

Answer from: Quest

solution:

the given function is ,

$f(x) = 4 x^3 - 72 x^2 + 320 x,$

= $4x( x^2- 18 x + 80)\\\\ 4 x(x^2-10 x -8 x + 80) \\\\ 4 x[(x-10)(x-8)]$

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

$f(x) = a x^3+ b x^2 + c x+d,$

sum of the roots = a + b +c= 0+8+10=18= $\frac{-b}{a}$

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 = $\frac{c}{a}$

product of roots = a b c = 0= $\frac{d}{a}$

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function $f(x) = 4 x^3 - 72 x^2 + 320 x,$ is given by entry and exit route of this hall.

Answer from: Quest

the system of inequalities is

$y> (1/3)x$

$y\leq-x+4$

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

$m=y/x=1/3$

the equation of the dashed line is

$y=(1/3)x$

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

$y> (1/3)x$

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

$m=(4-0)/(0-4)=-1$

the equation of the solid line is

$y=-x+4$

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

$y\leq-x+4$

step 3

the system of inequalities is

$y> (1/3)x$

$y\leq-x+4$

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