I have a word problem I am not able to work. The problem is: You are designing greeting cards on your computer to raise money for a charity. You buy card stock at a cost of $.50 per card and rent a table at the fundraiser for $20. You will sell the cards in sets of 12 for $10.20. How many sets of cards do you have to sell in order to make more than what you spend? So far the equation I have is .50x + 20 <. I don't know what is next or if I am totally wrong. Can you help?
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Word Problem
- Thread starter Mary
- Start date
Formally you are correct that this problem must be set up as an inequation. And you can set it up in terms of numbers of cards.I have a word problem I am not able to work. The problem is: You are designing greeting cards on your computer to raise money for a charity. You buy card stock at a cost of $.50 per card and rent a table at the fundraiser for $20. You will sell the cards in sets of 12 for $10.20. How many sets of cards do you have to sell in order to make more than what you spend? So far the equation I have is .50x + 20 <. I don't know what is next or if I am totally wrong. Can you help?
0.50x + 20 expresses cost in terms of number of cards.
The other side of the inequation must be what you earn in terms of number of cards if you are expressing costs in terms of cards. Must compare apples to apples. Please answer as many of the questions below as possible.
How much are you selling each card for?
So what is is your inequation?
Can you solve it?
If so, what do you get?
Notice, however, that the problem asks for number of sets of twelve so you are not done yet.
What's the answer?
Now it's easier to set the problem up in terms of sets in the first place. How would you do that?
Formally you are correct that this problem must be set up as an inequation. And you can set it up in terms of numbers of cards.
0.50x + 20 expresses cost in terms of number of cards.
The other side of the inequation must be what you earn in terms of number of cards if you are expressing costs in terms of cards. Must compare apples to apples. Please answer as many of the questions below as possible.
How much are you selling each card for?
So what is is your inequation?
Can you solve it?
If so, what do you get?
Notice, however, that the problem asks for number of sets of twelve so you are not done yet.
What's the answer?
Now it's easier to set the problem up in terms of sets in the first place. How would you do that?
It is inequalities we are working with but I still can't figure out what the last part of the problem is. Each card is sold for $.85
Yes, each card is sold for $0.85. So the money earned for selling x cards is 0.85x, right. 85 cents is brought in for each card sold.It is inequalities we are working with but I still can't figure out what the last part of the problem is. Each card is sold for $.85
You should get in the habit on every word problem of WRITING down what each letter stands for.
x = number of cards made and sold.
Now translate the information given in words into mathematical form. Again do this in writing.
cost = 20 + 0.5x.
money earned = 0.85x.
You want to know when the money earned is greater than the cost so
20 + 0.5x < 0.85x.
Now solve. Can you do that?
Unfortunately, as denis and I have both said, this does not quite solve the problem because it asks for the number of sets, not the number of cards.
Yes, each card is sold for $0.85. So the money earned for selling x cards is 0.85x, right. 85 cents is brought in for each card sold.
You should get in the habit on every word problem of WRITING down what each letter stands for.
x = number of cards made and sold.
Now translate the information given in words into mathematical form. Again do this in writing.
cost = 20 + 0.5x.
money earned = 0.85x.
You want to know when the money earned is greater than the cost so
20 + 0.5x < 0.85x.
Now solve. Can you do that?
Unfortunately, as denis and I have both said, this does not quite solve the problem because it asks for the number of sets, not the number of cards.
The equation is. .50x + 20 < .85 X<57. So the answer is 5 or more sets! Thank you very much for your help!!
Last edited:
Actually the answer isThe equation is. .50x + 20 < .85 X<57. So the answer is 5 or more sets! Thank you very much for your help!!
\(\displaystyle 0.5x + 20 < 0.85x \implies 20 < 0.85x - 0.5x = 0.35x \implies \dfrac{20}{0.35} < x \implies 57.14 < x.\)
So yes the number of sets is 5. But the way you laid out your answer might prevent you from getting partial credit on some problems in a test.