**Problem Description:****Show AND explain your work. Write a system of equations to represent the situation and solve using the Substitution Method.****The Math Club is baking for a bake sale. The fruit-pie recipe calls for twice as many peaches as nectarines. If it takes a total of 168 pieces of fruit for all of the pies, how many nectarines are needed?****Solution:**1. Let's denote the number of nectarines as $ N $.2. The number of peaches will be $ 2N $ as the recipe calls for twice as many peaches as nectarines.**System of Equations:**1. $ P = 2N $ (Equation 1)2. $ N + P = 168 $ (Equation 2)**Substitution Method:**First, solve Equation 1 for $ P $:\[ P = 2N \]Next, substitute $ P = 2N $ into Equation 2:\[ N + 2N = 168 \]Combine like terms:\[ 3N = 168 \]Divide both sides by 3:\[ N = \frac{168}{3} \]\[ N = 56 \]So, the number of nectarines needed is $ 56 $.

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Show AND explain your work. Write a system of equations to represent the situation and solve using Substitution Method. The Math Club is baking for a bake sale. The fruit-pie recipe calls for twice as many peaches as nectarines. If it takes a total of 168 pieces of fruit for all of the pies, how many nectarines are needed?

Show AND explain your work. Write a system of equations to represent the situation and solve using Substitution Method. The Math Club is baking for a bake sale. The fruit-pie recipe calls for twice as many peaches as nectarines. If it takes a total of 168 pieces of fruit for all of the pies, how many nectarines are needed?

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

**Problem Description:**

**Show AND explain your work. Write a system of equations to represent the situation and solve using the Substitution Method.**

**The Math Club is baking for a bake sale. The fruit-pie recipe calls for twice as many peaches as nectarines. If it takes a total of 168 pieces of fruit for all of the pies, how many nectarines are needed?**

**Solution:**

1. Let's denote the number of nectarines as $ N $.
2. The number of peaches will be $ 2N $ as the recipe calls for twice as many peaches as nectarines.

**System of Equations:**

1. $ P = 2N $ (Equation 1)
2. $ N + P = 168 $ (Equation 2)

**Substitution Method:**

First, solve Equation 1 for $ P $:
\[ P = 2N \]

Next, substitute $ P = 2N $ into Equation 2:
\[ N + 2N = 168 \]

Combine like terms:
\[ 3N = 168 \]

Divide both sides by 3:
\[ N = \frac{168}{3} \]
\[ N = 56 \]

So, the number of nectarines needed is $ 56 $.

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