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One cookbook recommends that a person can substitute 1 tablespoon (Tbsp) of dried mint leaves for 
(1)/(4) cup (c) of fresh mint leaves. The salad recipe calls for 
2Tbsp of fresh mint leaves. How many Tbsp of dried mint leaves could a person substitute into the recipe?
(There are 
16Tbsp in 
1c.)

One cookbook recommends that a person can substitute 11 tablespoon (Tbsp\mathrm{Tbsp} ) of dried mint leaves for 14 \frac{1}{4} cup (c) of fresh mint leaves. The salad recipe calls for 2 2 Tbsp\mathrm{Tbsp} of fresh mint leaves. How many Tbsp\mathrm{Tbsp} of dried mint leaves could a person substitute into the recipe?\newline(There are 16 16 Tbsp\mathrm{Tbsp} in 1c 1 \mathrm{c} .)

Full solution

Q. One cookbook recommends that a person can substitute 11 tablespoon (Tbsp\mathrm{Tbsp} ) of dried mint leaves for 14 \frac{1}{4} cup (c) of fresh mint leaves. The salad recipe calls for 2 2 Tbsp\mathrm{Tbsp} of fresh mint leaves. How many Tbsp\mathrm{Tbsp} of dried mint leaves could a person substitute into the recipe?\newline(There are 16 16 Tbsp\mathrm{Tbsp} in 1c 1 \mathrm{c} .)
  1. Understand Conversion Ratio: First, we need to understand the conversion ratio given by the cookbook. It states that 11 tablespoon (Tbsp) of dried mint leaves is equivalent to 14\frac{1}{4} cup (c) of fresh mint leaves. We also know that there are 1616 tablespoons in 11 cup.
  2. Convert Fresh Mint to Tablespoons: First, we convert the 14\frac{1}{4} cup of fresh mint leaves to tablespoons using the conversion that 11 cup equals 1616 tablespoons. So, 14\frac{1}{4} cup is equal to 16Tbsp16 \, \text{Tbsp} divided by 44.
  3. Calculate Conversion: Calculating the conversion: \newline16Tbsp4=4Tbsp\frac{16 \, \text{Tbsp}}{4} = 4 \, \text{Tbsp} \newlineThis means that 14cup\frac{1}{4} \, \text{cup} of fresh mint leaves is equivalent to 4tablespoons4 \, \text{tablespoons} of fresh mint leaves.
  4. Set Up Proportion for Recipe: Now, we know that 11 Tbsp of dried mint is equivalent to 44 Tbsp of fresh mint. The recipe calls for 22 Tbsp of fresh mint. To find out how many tablespoons of dried mint this is equivalent to, we set up a proportion: \newline1 Tbsp dried4 Tbsp fresh=x Tbsp dried2 Tbsp fresh\frac{1 \text{ Tbsp dried}}{4 \text{ Tbsp fresh}} = \frac{x \text{ Tbsp dried}}{2 \text{ Tbsp fresh}}.
  5. Calculate Equivalent Amount: Solving for xx gives us x=(1 Tbsp dried4 Tbsp fresh)×2 Tbsp freshx = (\frac{1 \text{ Tbsp dried}}{4 \text{ Tbsp fresh}}) \times 2 \text{ Tbsp fresh}. \newlineCalculating xx: \newlinex=(14)×2=12x = (\frac{1}{4}) \times 2 = \frac{1}{2} \newlineThis means that 12\frac{1}{2} tablespoon of dried mint leaves can be used to substitute for 22 tablespoons of fresh mint leaves.

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