in a bakery,  4 cupcakes is sold for $2.10 and 3 tarts is sold for $1.60. Mrs Lee spent a total of $203.60 on some cupcakes and tarts at the bakery.  she repacks them onto trays such that there are 3 cupcakes and 5 tarts on each tray for a party.  how many tarts did she buy from the bakery?  explain using ratio

Let’s begin by breaking down the problem into smaller steps:

### Step 1: Determine the price per cupcake and per tart.
- 4 cupcakes are sold for $2.10, so the price per cupcake is:
  \[
  \frac{2.10}{4} = 0.525 \, \text{dollars per cupcake}.
  \]

- 3 tarts are sold for $1.60, so the price per tart is:
  \[
  \frac{1.60}{3} = 0.5333 \, \text{(repeating)} \, \text{dollars per tart}.
  \]

### Step 2: Define variables for the number of cupcakes and tarts.
Let:
- $ x $ be the number of cupcakes Mrs. Lee bought.
- $ y $ be the number of tarts Mrs. Lee bought.

### Step 3: Express total cost in terms of cupcakes and tarts.
The total cost of cupcakes and tarts is given as $203.60. Therefore:
\[
0.525x + 0.5333y = 203.60.
\]

### Step 4: Use the repacking information to form a ratio.
Mrs. Lee repacked the cupcakes and tarts into trays, with 3 cupcakes and 5 tarts per tray. This implies that the number of cupcakes is to the number of tarts as 3 is to 5, or:
\[
\frac{x}{y} = \frac{3}{5}.
\]

This can be rewritten as:
\[
x = \frac{3}{5}y.
\]

### Step 5: Substitute $ x $ into the cost equation.
Substitute $ x = \frac{3}{5}y $ into the total cost equation:
\[
0.525\left(\frac{3}{5}y\right) + 0.5333y = 203.60.
\]

Simplify the equation:
\[
0.315y + 0.5333y = 203.60,
\]
\[
0.8483y = 203.60.
\]

### Step 6: Solve for $ y $.
Now, solve for $ y $:
\[
y = \frac{203.60}{0.8483} \approx 240.
\]

Thus, Mrs. Lee bought **240 tarts** from the bakery.

### Step 7: Verify the number of cupcakes.
Using the relationship $ x = \frac{3}{5}y $:
\[
x = \frac{3}{5} \times 240 = 144.
\]

### Final Check:
- The cost of 144 cupcakes is:
  \[
  144 \times 0.525 = 75.60.
  \]
- The cost of 240 tarts is:
  \[
  240 \times 0.5333 \approx 128.00.
  \]
- The total cost is:
  \[
  75.60 + 128.00 = 203.60.
  \]

Thus, everything checks out correctly!

### Conclusion:
Mrs. Lee bought **240 tarts** from the bakery.

Would you like further details or explanations?

Here are some related questions for further practice:


In a bakery, 4 cupcakes are sold for $2.10 and 3 tarts are sold for $1.60. Mrs. Lee spent a total of $203.60 on some cupcakes and tarts at the bakery. She repacks them onto trays such that there are 3 cupcakes and 5 tarts on each tray for a party. How many tarts did she buy from the bakery? Explain using ratio.

Learn how to solve a real-life word problem involving ratios and linear equations. Mrs. Lee buys cupcakes and tarts for a total of $203.60, and we use algebraic methods to determine how many tarts she purchased. Detailed step-by-step explanation included. Suitable for students in Grades 8-10.

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