# MangaMathSpark Problem: Valentine's Day Chocolate Box Challenge

Updated by Michelle

By Michelle Kueh, VP (Mangahigh.com) | Published February 6th, 2024

### Valentine's Day Chocolate Box Challenge

Sarah wants to buy a special box of chocolates for her friends on Valentine's Day. The local candy store offers a variety of chocolates in different shapes and flavors. She decides to create a custom box with a mix of these chocolates. The prices are as follows:

• Heart-shaped Milk Chocolate: \$0.50 each
• Rose-shaped Dark Chocolate: \$0.75 each
• Star-shaped White Chocolate: \$0.65 each

Sarah has a budget of \$10. She wants to include at least one of each type of chocolate in her box.

1. (Easy) Budgeting: Help Sarah calculate how many of each type of chocolate she can buy without exceeding her budget.
2. (Medium) Proportion: If Sarah wants the box to have twice as many milk chocolates as dark chocolates and the same number of white chocolates as dark chocolates, how many of each should she buy?
3. (Hard) Comparison: If the store offers a pre-made Valentine’s Day chocolate box containing 5 heart-shaped milk chocolates, 3 rose-shaped dark chocolates, and 2 star-shaped white chocolates for \$8, should Sarah buy the pre-made box or make her own based on the proportions she wants? Which option gives her more chocolates for her money?

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#### SOLUTION

##### Budgeting:

Sarah can buy a maximum of 20 heart-shaped milk chocolates, 13 rose-shaped dark chocolates, and 15 star-shaped white chocolates individually without exceeding her \$10 budget.

##### Proportion:

Based on Sarah's desired proportions (twice as many milk chocolates as dark chocolates and the same number of white chocolates as dark chocolates), she can buy 8 heart-shaped milk chocolates, 4 rose-shaped dark chocolates, and 4 star-shaped white chocolates within her budget.

##### Comparison:

The pre-made Valentine’s Day chocolate box contains 5 heart-shaped milk chocolates, 3 rose-shaped dark chocolates, and 2 star-shaped white chocolates for \$8, totaling 10 chocolates.

Sarah's custom box, based on her proportions, totals 16 chocolates for her \$10 budget, offering her 6 more chocolates than the pre-made box for an additional \$2.

Conclusion: Sarah should create her own box based on the proportions she wants, as it gives her more chocolates for her money compared to the pre-made box.