Q41. On the first day, a total of 40 ... [FREE SOLUTION]

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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 6: Q41. (page 390)

On the first day, a total of 40 items were sold for $$356$ . Define the variables, and write equations to find the number of cakes and pies sold. Solve by using elimination.
Monarch Middle School
Bake sale
Pies
$$ 10$
Cakes
$$ 8$

Short Answer

Expert verified

The number of cakes and pies sold are 22 and 18 respectively.

Step by step solution

Step 1. State the concept of elimination method.

The elimination method is the method in which addition or subtraction method is used to get an equation in the one variable.

If the coefficients are opposite, use the addition and when the coefficients are same, use the subtraction.

Step 2. Add or subtract the equations to eliminate one variable.

Let the number of cakes be $x$ and the number of pies be $y$ .

As per the conditions the system of equations thus formed will be:

$x + y = 40$ 鈥� (1)

$8 x + 10 y = 356$ 鈥� (2)

Multiply equation (1) by 8.

$\begin{matrix} 8 (x + y) = 8 脳 (40) \\ 8 x + 8 y = 320 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌� (3) \end{matrix}$

Note that both the equations (2) and (3) havelocalid="1647579462957" $8 x$ in same sign, therefore, variablelocalid="1647579475744" $x$ can be eliminated if both equations are subtracted.

$\begin{array}{l} 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌� 8 x + 8 y = 320 \\ \underset{炉}{(鈭�) 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌� 8 x + 10 y = 356} \\ 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆€� 鈭� 2 y = 鈭� 36 Dividebothsidesby-2 \\ 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆€夆€夆€� y = 18 \end{array}$

Step 3. Solve for x.

Substitute 18 for $y$ into the equation (1) and solve for $x$ .

$\begin{matrix} x + y = 40 \\ x + (18) 鈭� 18 = 40 鈭� 18 \\ x = 22 \end{matrix}$

Therefore, the number of cakes and pies sold are 22 and 18 respectively.

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91影视

On the first day, a total of 40 items were sold for $\(356$ . Define the variables, and write equations to find the number of cakes and pies sold. Solve by using elimination.
Monarch Middle School
Bake sale
Pies
$\) 10$
Cakes
$$ 8$

Short Answer

Step by step solution

Step 1. State the concept of elimination method.

Step 2. Add or subtract the equations to eliminate one variable.

Step 3. Solve for x.

One App. One Place for Learning.

Most popular questions from this chapter

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91影视

On the first day, a total of 40 items were sold for\(356. Define the variables, and write equations to find the number of cakes and pies sold. Solve by using elimination.Monarch Middle SchoolBake salePies\)10Cakes$8

Short Answer

Step by step solution

Step 1. State the concept of elimination method.

Step 2. Add or subtract the equations to eliminate one variable.

Step 3. Solve for x.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Geometry

Decision Maths

Calculus

Pure Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

On the first day, a total of 40 items were sold for $\(356$ . Define the variables, and write equations to find the number of cakes and pies sold. Solve by using elimination.
Monarch Middle School
Bake sale
Pies
$\) 10$
Cakes
$$ 8$