Question

It should be a simple problem, but I come up with 2 possible solutions. Solution a seems correct but I can't figure out why Solution b doesn't work.

36 chocolate bars each weigh 1.55 oz. The total cost of all 36 bars is $23.20. What is the price per pound.

Solution a: 36 bars divided by $23.20 equals approximately $1.55. The bars are 1.55 oz so the cost is 1$ per oz or 16$ per pound

Solution b: 36 bars multiplied by 1.55 oz equals 55.8 oz. 55.8 total oz divided by $23.20 equals $2.40 per oz or $38.40 per pound

Answer 1

weight\[=\frac{ 36*1.55 }{ 16 }=\frac{ 13.95 }{ 4 } lbs\]
Price per pound
\[=23.20 \div \frac{ 13.95 }{ 4 }=23.20\times \frac{ 4 }{ 13.95 }=\frac{ 2320 }{ 100 }*\frac{ 400 }{ 1395 }=?\]

Answer 2

Divide the cost by the number of bars to get the price per bar.
Then divide that by 1.55 oz to get the cost per ounce.
Then multiply by 16 to get the cost per lb.

Answer 3

Both of your calculations are incorrect.

Answer 4

$6.65/lb

Answer 5

Here are your errors:
a. You are looking for cost per lb.
You need to divide dollars per weight.
You divided 36 by $23.20
That gives you the number of bars per dollar.
You got approximately 1.55. That means you can buy approx. 1.55 bars per dollar.
This is not 1.55 oz per dollar since each bar itself is 1.55 oz.
1.55 bar per dollar means 1.55 * 1.55 oz per dollar = 2.4 oz/dollar

Answer 6

You are correct now.
$6.65/lb is correct.

Answer 7

Thank you

Answer 8

In solution b., you started correctly. 36 bars times 1.55 oz is 55.8 oz.
Then you made the same mistake as before. You divided oz by dollars.
That gives you the rate of weight per price.
That's not what you want. You want price per weight.
You need to divide $23.20 by 55.8 oz to get 0.416 dollars per ounce.
Since there are 16 oz in a lb, the price per lb is 16 times the price per oz.
Then multiply 0.416 $/oz by 16 to get $6.65 $/lb

Answer 9

You're welcome.

Answer 10

For rate problems you always need to see what the final units are.
If you are asked a speed (for example in miles per hour), then you must divide miles by hours, not hours by miles.