Question

Dwayne buys 1 loaf of bread and 6 eggs for $4.45. Sheila buys 1 loaf of bread and 1 dozen eggs for $5.65. Let x be the cost, in dollars, of a loaf of bread. Let y be the cost, in dollars, of an egg.

ANSWER ALL 3 PARTS SEPARATELY.
PART 1: Write a system of equations that represents this situation.
PART 2: Solve the system of equations to find how much the store charges for bread and for eggs.
PART 3: Calculate how much Mina pays for 3 loaves of bread and 2 dozen eggs.

Answer 1

To solve the system of equations, we set up two equations based on purchases made by Dwayne and Sheila. Solving these equations, we find that a loaf of bread costs $3.25 and an egg costs $0.20. Using these prices, Mina's cost for 3 loaves of bread and 2 dozen eggs is $14.55.

Step-by-step explanation:

To solve this system of equations question, we'll start by setting up two equations based on the information provided. The question tells us that Dwayne buys 1 loaf of bread and 6 eggs for $4.45 and Sheila buys 1 loaf of bread and a dozen eggs for $5.65.

Part 1: Writing the System of Equations

Let x be the cost of a loaf of bread and y be the cost of an egg. The equations would be:

1x + 6y = 4.45 (Dwayne's purchase)

1x + 12y = 5.65 (Sheila's purchase)

Part 2: Solving the System of Equation

Using the substitution or elimination method, we can find the values for x and y that satisfy both equations. If we subtract the first equation from the second, we get:

1x + 12y - (1x + 6y) = 5.65 - 4.45

6y = 1.20

y = 1.20 / 6

y = 0.20

Now that we know the cost of an egg, we can substitute y into one of the equations to find x:

1x + 6(0.20) = 4.45

1x + 1.20 = 4.45

x = 4.45 - 1.20

x = 3.25

Part 3: Calculating the Cost for Mina's Purchase

Mina buys 3 loaves of bread and 2 dozen eggs, which would cost:

3x + 24y = 3(3.25) + 24(0.20) = 9.75 + 4.80

The total cost is $14.55.