Which equation represents the solution to the following?
I have some lemons. Jill has two more limes than five times the number of lemons that I have. Emma has one-third as many limes as Jill. Emma has 4 limes. How many lemons do I have?
x = your lemons
j = 5x + 2 = Jill'ls limes
e = (5x + 2) / 3 = Emma's limes
e = 4
(5x + 2) / 3 = 4
5x + 2 = 12
5x = 10
x = 2
Let's break down the information given in the problem:
1. Jill has two more limes than five times the number of lemons that I have.
Let's say I have "x" lemons. According to the problem, Jill has 2 more limes than five times the number of lemons I have, so Jill has 5*x + 2 limes.
2. Emma has one-third as many limes as Jill.
We know that Jill has 5*x + 2 limes, so according to the problem, Emma has (1/3) * (5*x + 2) limes.
3. Emma has 4 limes.
Given that Emma has (1/3) * (5*x + 2) limes, we can set up the equation: (1/3) * (5*x + 2) = 4.
To find the number of lemons you have (represented by "x"), we need to solve the equation. We can do this by following these steps:
1. Multiply both sides of the equation by 3 to get rid of the fraction: 3 * (1/3) * (5*x + 2) = 3 * 4.
Simplifying, we have: 5*x + 2 = 12.
2. Subtract 2 from both sides of the equation to isolate the term with "x": 5*x + 2 - 2 = 12 - 2.
Simplifying, we have: 5*x = 10.
3. Divide both sides of the equation by 5 to solve for "x": (5*x)/5 = 10/5.
Simplifying, we have: x = 2.
Therefore, the solution to the problem is that you have 2 lemons.