Question

Divide 170 into three parts such that the first part is 10 more than that the second part and its ratio with third part is 2:5

Answer 1

The three parts can be written as 2x, 2x-10 and 5x.

2x + (2x-10) +5x = 170

9x - 10 = 170

9x =180, so x=20

Thus the three parts are 40, 30 and 100.

Answer 2

Answer:

Here we should find three parts value from the given information in the question.

Final Answer:

• first part $f=40$  
• second part  $s=30$
• third part $t=100$                            

Step-by-step explanation:

Given:

• Let first part $=f$
• second part $=s$
• third part $=t$
• Divide 170 into three parts.That is,

           first part + second part + third part = 170

            $f+s+t=170$    -------------(1)

• first part is 10 more than that the second part.That is,

                       $f=10+s$   --------------(2)

• ​ratio of first part and third part = $2:5$. That is,

                       $\frac{f}{t} =\frac{2}{5}$      -----------------(3)

To find: first part(f),second part(s) and third part(t) value.

Solution:

Step 1:

• To find the third part value from equation(3). That is,

                 $\frac{f}{t} =\frac{2}{5}$

• Apply equation(2) in the above equation.

             $\frac{10+s}{t} =\frac{2}{5}$

                  $t =\frac{5(10+s)}{2}$

Step 2:

• Now apply the first part, second part and third part value in equation(1).That is,
• first part $=10+s$ (from equation 2), second part $=s$, thirt part $=\frac{5(10+s)}{2}$

equation(1)

   $(10+s)+s+\frac{5(10+s)}{2} =170$

Step 3:

• Take the L.C.M for step 2 answer. That is,

         $\frac{(20+2s)+2s+5(10+s)}{2} =170$

             $\frac{20+2s+2s+50+5s}{2} =170$

                            $\frac{9s+70}{2} =170$

Step 4:

• Next we should do the cross multiplication.

                           $9s+70 =170\times2$

                           $9s+70 =340$

                                   $9s=340-70$

                                   $9s=270$

                                     $s=\frac{270}{9}$

              second part  $s=30$

Step 5:

• Now we can find the value of first part value(f) from the equation(2).

                                    $f=10+s$

                                    $f=10+30$  

                    first part $f=40$      

Step 6:    

• Now we can find the value of third part value(t) from the equation(3).

                                    $\frac{f}{t} =\frac{2}{5}$  

                                   $\frac{40}{t} =\frac{2}{5}$

                                     $t =\frac{5}{2}\times 40$

                                     $t =5\times 20$

                    third part $t=100$

Final Answer:

• first part $f=40$  
• second part  $s=30$
• third part $t=100$

                               

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