Sam had 2 boxes of cookies.Box A contained 55 more cookies than Box B at first.Sam transferred 310 cookies from Box A to Box B.In the end,the ratio of the number of cookies in Box B to the number of bookies in Box A was 6:1.

Question

a)How many fewer cookies were there in Box A than in Box B in the end?
b)How many cookies were there in the two cookies altogether?

Answer 1

Let's use algebra to solve this problem.

1. Let's start by setting up some variables:

- Let B = the number of cookies in Box B at first
- Then A = B + 55 (since Box A had 55 more cookies than Box B at first)

2. After Sam transfers 310 cookies from Box A to Box B:

- Box B now has B + 310 cookies
- Box A now has A - 310 cookies, which is (B + 55) - 310

3. The problem tells us that the ratio of cookies in Box B to Box A is 6:1 in the end. We can set up an equation for this:

- (B + 310) / (B + 55 - 310) = 6/1

4. Now we can solve for B:

- Cross-multiplying gives us (B + 310) = 6(B - 255)
- Expanding the brackets and simplifying gives us 4B = 2190
- So B = 547.5 (we get a decimal here, but remember that we can't have half a cookie, so we'll round up to the nearest whole number)

5. We can use this value of B to find A:

- A = B + 55 = 602.5 (rounding up again)

6. Now we can answer the questions:

a) How many fewer cookies were there in Box A than in Box B in the end?

- Box A had 602.5 cookies and Box B had 547.5 cookies, so there were 55 fewer cookies in Box B than in Box A in the end.

b) How many cookies were there in the two boxes altogether?

- Box A had 602.5 cookies and Box B had 547.5 cookies, so together they had 1150 cookies.