Shayden had $243. He spent 2/9 of his money to buy 5 chocolate bars and 6 packets of potato chips. The cost of 3 packets of potato chips was the same as the cost of 2 chocolate bars. Find the greatest number of chocolate bars that he could buy with the money he had left.
Let's break down the problem step by step:
Step 1: Calculate the amount Shayden spent
Shayden spent 2/9 of his money on 5 chocolate bars and 6 packets of potato chips.
The cost of 3 packets of potato chips was the same as the cost of 2 chocolate bars.
Let x be the cost of 1 packet of chips.
Then the cost of 3 packets of chips would be 3x.
And the cost of 2 chocolate bars would also be 3x.
So, Shayden spent 2/9 * $243 = ($243/9) * 2 = $54 on 5 chocolate bars and 6 packets of potato chips.
Step 2: Calculate the cost of the chocolate bars
Since the cost of 2 chocolate bars is 3x, we can assume that the cost of 1 chocolate bar is (3x/2).
Step 3: Calculate the cost of 1 packet of chips
If the cost of 3 packets of chips is 3x, then the cost of 1 packet would be (3x/3) = x.
Step 4: Calculate the cost of 6 packets of chips
The cost of 6 packets of chips would be 6x.
Step 5: Calculate the total amount spent on chocolate bars and chips
Shayden spent $54, which means the total cost of 5 chocolate bars and 6 packets of chips is (3x/2) * 5 + 6x = (15x/2) + 6x = (15x + 12x)/2 = 27x/2.
Step 6: Set up an equation to find the value of x
We know that Shayden spent $54, so (15x + 12x)/2 = 54.
Step 7: Solve the equation
27x/2 = 54
27x = 2 * 54
27x = 108
x = 108/27
x = 4.
Step 8: Calculate the cost of 1 chocolate bar
The cost of 1 chocolate bar would be (3x/2) = (3 * 4)/2 = 6.
Step 9: Calculate the maximum number of chocolate bars that Shayden could buy with the money he had left
Shayden had $243 and spent $54 on 5 chocolate bars and 6 packets of chips.
So, he had $243 - $54 = $189 left.
The maximum number of chocolate bars he can buy with $189 is 189/6 = 31.5
Since we can't have a fractional number of chocolate bars, the greatest number of chocolate bars that Shayden could buy with the money he had left is 31.
Therefore, Shayden can buy a maximum of 31 chocolate bars with the money he had left.
Shayden spent 2/9 x $243 = $<<2/9*243=54>>54 on chocolate bars and potato chips.
The cost of each chocolate bar is $54/5 = $<<54/5=10.80>>10.80.
The cost of 3 packets of potato chips is $54/6 = $<<54/6=9>>9.
Therefore, the cost of 2 chocolate bars is $9.
The cost of 1 chocolate bar is $9/2 = $<<9/2=4.50>>4.50.
Hence, Shayden could buy $243/$4.50 = <<243/4.5=54>>54 chocolate bars.
Therefore, the greatest number of chocolate bars Shayden could buy with the money he had left is 54. Answer: \boxed{54}.
To find the greatest number of chocolate bars that Shayden could buy with the money he had left, let's break down the problem step by step.
1. Shayden spent 2/9 of his money on 5 chocolate bars and 6 packets of potato chips. This means that the total cost of the chocolate bars and potato chips was 2/9 of $243.
Cost of chocolate bars + Cost of potato chips = (2/9) * $243
2. The cost of 3 packets of potato chips was the same as the cost of 2 chocolate bars.
Cost of 3 packets of potato chips = Cost of 2 chocolate bars
Now, let's try solving the problem.
Step 1: Calculate the total cost of the chocolate bars and potato chips.
Total cost = (2/9) * $243
Step 2: To find the cost of each chocolate bar and packet of potato chips, divide the total cost by the sum of their quantities.
Cost of each chocolate bar/packet of chips = Total cost / (5 + 6)
Step 3: Since the cost of 3 packets of potato chips is the same as the cost of 2 chocolate bars, we can set up an equation:
3 * (Cost of each packet of chips) = 2 * (Cost of each chocolate bar/packet of chips)
Step 4: Solve the equation to find the cost of each packet of chips and each chocolate bar.
Cost of each packet of chips = (2/3) * (Cost of each chocolate bar/packet of chips)
Step 5: Calculate how many chocolate bars Shayden could buy with the money he had left.
Money left = $243 - Total cost of chocolate bars and chips
Number of chocolate bars = Money left / Cost of each chocolate bar
By following these steps, you should be able to find the greatest number of chocolate bars that Shayden could buy with the money he had left.