Question

tasty treats sells a standard trail mix with no chocolate and a sweet trail mix that adds chocolate to the standard trail mix. in the sweet trail mix, the ratio of ounces of chocolate to ounces of standard trail mix is 2 to 3. katie orders a bag of sweet trail mix that contains 54 ounces of standard trail mix. how many ounces of chocolate are in katies bag of sweet trail mix? a 18 oz b 32 oz c 81 oz d 36 oz wildcat doughnuts sells a “baker’s dozen” (13) variety box of plain glazed and iced doughnuts for $6.99. the ratio of iced doughnuts to total doughnuts is 5 to 13. calzone middle school ordered several of these variety boxes for breakfast one morning during teacher appreciation week. what could be the number of plain glazed doughnuts that calzone middle school had in their order? (choose 2.) a 39 c 20 e 48 b 32 d 52 f 26

Explanation:

First Sub - Question (Trail Mix Problem)

Step1: Define the ratio relationship

The ratio of chocolate to standard trail mix is \(2:3\). Let the ounces of chocolate be \(x\) and the ounces of standard trail mix be \(54\) (given). So we can set up a proportion \(\frac{x}{54}=\frac{2}{3}\).

Step2: Solve the proportion

Cross - multiply: \(3x = 54\times2\). Then \(3x=108\). Divide both sides by 3: \(x=\frac{108}{3}=36\).

Step1: Find the number of plain glazed doughnuts per box

The total number of doughnuts per box is 13, and the ratio of iced doughnuts to total doughnuts is \(5:13\). So the number of iced doughnuts per box is 5, and the number of plain glazed doughnuts per box is \(13 - 5=8\).

Step2: Analyze the number of plain glazed doughnuts in multiple boxes

The number of plain glazed doughnuts in \(n\) boxes will be \(8n\), which means the number of plain glazed doughnuts must be a multiple of 8.

• For option A: \(39\div8 = 4.875\) (not a multiple of 8)
• For option B: \(32\div8 = 4\) (multiple of 8)
• For option C: \(20\div8 = 2.5\) (not a multiple of 8)
• For option D: \(52\div8 = 6.5\) (not a multiple of 8)
• For option E: \(48\div8 = 6\) (multiple of 8)
• For option F: \(26\div8 = 3.25\) (not a multiple of 8)

Answer:

D. 36 oz

Second Sub - Question (Doughnut Problem)