maya and winston share some cookies in the ratio 2:3. maya had 3 fewer cookies than winston how many cookies they share altogether?
2:3 = 6:9
6 + 9 = ?
Let's assume that Maya has 2x cookies and Winston has 3x cookies.
Given that Maya had 3 fewer cookies than Winston, we can set up the equation:
2x = (3x) - 3
Simplifying the equation, we get:
2x - 3x = -3
-x = -3
Multiplying both sides of the equation by -1, we get:
x = 3
This means that Maya has 2x = 2(3) = 6 cookies and Winston has 3x = 3(3) = 9 cookies.
Together, they have 6 + 9 = 15 cookies.
To solve this problem, we need to follow a few steps.
Step 1: Assign variables to the unknown quantities. Let's call the number of cookies Maya has 'm' and the number of cookies Winston has 'w'.
Step 2: Translate the given information into equations. We know that "Maya had 3 fewer cookies than Winston." This can be written as:
m = w - 3
We also know that they share the cookies in the ratio 2:3. This means that for every 2 cookies Maya has, Winston has 3 cookies. We can write this as:
m/2 = w/3
Step 3: Solve the system of equations. We have two equations:
m = w - 3
m/2 = w/3
We can solve this system by substitution. Rearrange the first equation to get:
w = m + 3
Substitute this expression for 'w' into the second equation:
m/2 = (m + 3)/3
Multiply both sides of the equation by 6 to eliminate the fractions:
3m = 2(m + 3)
Distribute on the right side of the equation:
3m = 2m + 6
Subtract 2m from both sides:
m = 6
Substitute this value back into the first equation to find w:
w = m + 3
w = 6 + 3
w = 9
So, Maya has 6 cookies and Winston has 9 cookies.
Step 4: Find the total number of cookies they share.
To find the total number of cookies they share, add the number of cookies Maya and Winston have:
Total cookies = Maya's cookies + Winston's cookies
Total cookies = 6 + 9
Total cookies = 15
Therefore, Maya and Winston share a total of 15 cookies.