SOLUTION: A bakery baked 1200 cupcakes and packed them into boxes. There were 5/8 as many big boxes as small boxes. Each big box contained 7 more cupcakes than each small box. There were 240

Question 1203188: A bakery baked 1200 cupcakes and packed them into boxes. There were 5/8 as many big boxes as small boxes. Each big box contained 7 more cupcakes than each small box. There were 240 more cupcakes packed in big boxes than in the small boxes. How many cupcakes were there in each small box?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
This may NOT be the most effective or neatest way to handle the problem:

Boxes CupcakesInBox CountCupcakes BIG BOX (5/8)b c+7 (5/8)b(c+7) SMALL BOX b c bc Total 1200

Simplifiable and and is system of two unknowns in two equations.
.
.
NOTICE THAT THIS SYSTEM APPEARS TO BE IN A FORMAT OF

which might be helpful.

---

Solving this

and then back-substituting

---

----which only means that 96 big boxes were used.

.
.
Would indicate 5 cupcakes in each small box.
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.
A bakery baked 1200 cupcakes and packed them into boxes.
There were 5/8 as many big boxes as small boxes.
Each big box contained 7 more cupcakes than each small box.
There were 240 more cupcakes packed in big boxes than in the small boxes.
How many cupcakes were there in each small box?
~~~~~~~~~~~~~~~~~

The problem is to solve in two steps.

First step Total x cupcakes packed in big boxes total y cupcakes packed in small boxes From the problem x + y = 1200 (1) x - y = 240 (2) Add equations (1) and (2). You will get 2x = 1440 --> x = 1440/2 = 720 (the number of cupcakes packed in big boxes) Then from eq(1) y = 1200 - x = 1200 - 720 = 480 (the number of cupcakes packed in small boxes). Second step Let z be the number of cupcakes in each small box (= the value under the problem's question) Then the number of cupcases in each big box is (z+7). The number of small boxes is (3) The number of big boxes is (4) According to 5the problem, the ratio of the number of big boxes (4) to the number of small boxes (3) is 5/8 = . Simplify and find z = 3z*8 = 5*2*(z+7) 24z = 10z + 70 24z - 10z = 70 14z = 70 z = 70/14 = 5. ANSWER. The number of cupcakes in each small box is 5 (five).

Solved.

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