Question

Jonathan has 30 chocolates. He gives some chocolates to his friend David. He then gives Sarah half the number of chocolates that he gave David and gives Lily two-thirds of what he gave David. After giving away the chocolates, Jonathan has 4 chocolates left. If the number of chocolates Jonathan gives David is x, which equation represents the situation? How many solutions does this equation have?

Answer 1

Answer:

equation which represent this situation is 30 - 13x/6 =4

Solution to this equation is x = 12

As we see that there is one equation and degree of x is one thus there is one solution.

Step-by-step explanation:

Total no. of chocolates with Jonathan = 30

 no. of chocolates given to David IS x

Given

He then gives Sarah half the number of chocolates that he gave David

no. of chocolates given to Sarah = 1/2 of no. of chocolates given to David

no. of chocolates given to Sarah = 1/2 of x = x/2

Again given

gives Lily two-thirds of what he gave David. After giving away the chocolates

no. of chocolates given to Lily = 2/3 of no. of chocolates given to David

no. of chocolates given to Lily = 2/3 of x = 2x/3

Total no. of chocolates given to David , Sarah and lily = x+x/2+2x/3

LCM of 2 and 3 is 6

                   

Total no. of chocolates given to David , Sarah and lily =( 6x + 3x+ 4x)/6

Total no. of chocolates given to David , Sarah and lily =13x/6

Now, additional information in the problem is

After giving away the chocolates, Jonathan has 4 chocolates left

Chocolate left with Jonathan = Total no. of chocolates with Jonathan  - Total no. of chocolates given to David , Sarah and lily

4 = 30 - 13x/6

=> 4 + 13x/6  = 30

=> 13x/6 = 30-4 = 26

=> x = 26*6/13 = 2*6 =12

Thus, equation which represent this situation is 30 - 13x/6 =4

Solution to this equation is x = 12

As we see that there is one equation and degree of x is one thus there is one solution.