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?

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.