Ratio-2
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Please show us what you have tried and exactly where you are stuck.
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https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520
Please share your work/thoughts about this problem.
Dr.Peterson
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I'll assume you are learning the beginnings of algebra. So let's use a variable. Suppose there are N cupcakes in all.
How many are in each big box? How many are in each small box? How many are in 3 big and 8 small boxes?
Now write and solve an equation.
If you aren't ready for equations with fractions, please let us know what methods you have been learning, so we can see what to suggest. This is why we want you to give us some information about your own thinking.
How many are in each big box? How many are in each small box? How many are in 3 big and 8 small boxes?
Now write and solve an equation.
If you aren't ready for equations with fractions, please let us know what methods you have been learning, so we can see what to suggest. This is why we want you to give us some information about your own thinking.
HallsofIvy
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- Jan 27, 2012
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Assuming you are just beginning algebra- the first question asked is "How many cupcakes did Patricia bake" so let X be the number of cupcakes Patricia baked- the value you want to find.
Now each sentence becomes an equation and each part of a sentence becomes an algebraic expression:
"She put half of the cupcakes equally into six boxes". Do you see that if there were X cupcakes, half of them is X/2? And dividing those, equally, into six boxes means there are (X/2)/6= X/12 cupcakes in each box?
"And the other half equally into 14 small boxes". Again, half the cupcakes is X/2 and, dividing those equally into 14 boxes means there are (X/2)/14= X/28 cupcakes in each small box.
Finally, "There were 34 cupcakes in 3 big boxes and 8 small boxes altogether". There were, from above, X/12 cupcakes in each big box so 3(X/12)= X/4 cupcakes in 3 big boxes. There were, from above, X/28 cupcakes in each small box so 8(X/28)= 2X/7 cupcakes in 8 small boxes. That is a total of X/4+ 2X/7. We are told that this is 34 so we have the equation X/4+ 2X/7= 34 to solve for X. I don't like fractions so I would start by multiplying both sides of that equation by 4(7)= 28.
Now each sentence becomes an equation and each part of a sentence becomes an algebraic expression:
"She put half of the cupcakes equally into six boxes". Do you see that if there were X cupcakes, half of them is X/2? And dividing those, equally, into six boxes means there are (X/2)/6= X/12 cupcakes in each box?
"And the other half equally into 14 small boxes". Again, half the cupcakes is X/2 and, dividing those equally into 14 boxes means there are (X/2)/14= X/28 cupcakes in each small box.
Finally, "There were 34 cupcakes in 3 big boxes and 8 small boxes altogether". There were, from above, X/12 cupcakes in each big box so 3(X/12)= X/4 cupcakes in 3 big boxes. There were, from above, X/28 cupcakes in each small box so 8(X/28)= 2X/7 cupcakes in 8 small boxes. That is a total of X/4+ 2X/7. We are told that this is 34 so we have the equation X/4+ 2X/7= 34 to solve for X. I don't like fractions so I would start by multiplying both sides of that equation by 4(7)= 28.