Question

Select the correct answer. 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? A. x + 1 2 ⁢ x + 2 3 ⁢ x = 30 − 4 , which has no solution B. x + 1 2 ⁢ x + 2 3 ⁢ x = 30 , which has infinitely many solutions C. x + 1 3 ⁢ x + 2 3 ⁢ x − 4 = 30 , which has one solution D. x + 1 2 ⁢ x + 2 3 ⁢ x + 4 = 30 , which has one solution E. 1 2 ⁢ x + 2 3 ⁢ x = x − 4 , which has no solution

Answer 1

The solution to equation x+ 1/2x+2/3x+4= 30 and has one solution x = 12 which is the correct answer would be an option (D).

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

Then Lily has two-thirds of what he has given David. Following the distribution of the chocolates,

The number of chocolates provided to Lily is equal to two-thirds of the number of chocolates given to David.

The number of chocolates given to Lily Equals 2/3 of x = 2x/3

Now, the total number of chocolates delivered to David, Sarah, and Lily

= x+x/2+2x/3

Here LCM of 2 and 3 is 6

The Total no. of chocolates given to David, Sarah, and lily

= (6x + 3x+ 4x)/6

The total number of chocolates distributed to David, Sarah, and Lily is 13x/6.

Jonathan had four chocolates left after giving them out.

The number of chocolates left with Jonathan equals the total number 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

⇒ x = 12

Hence, the equation which represents the given situation is 30 - 13x/6 =4

Learn more about the equations here;

brainly.com/question/10413253

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