Question

At the local market, five apples and six pears cost $10.94; one apple and three pears cost $334 Find the cost of one apple and one pear.

Answer 1

Let's denote the cost of one apple as "A" and the cost of one pear as "P".

Here are the given equations: Equation 1: 5A + 6P = $10.94 Equation 2: A + 3P = $3.34

To solve this system of equations, we can use the method of substitution or elimination. I will use the substitution method here.

First, let's solve Equation 2 for A in terms of P: A = $3.34 - 3P

Now substitute this value of A into Equation 1: 5($3.34 - 3P) + 6P = $10.94

Expand and simplify: $16.70 - 15P + 6P = $10.94 $16.70 - 9P = $10.94

Move $16.70 to the right side: -9P = $10.94 - $16.70 -9P = -$5.76

Divide both sides by -9: P = -$5.76 / -9 P ≈ $0.64

Now substitute this value of P back into Equation 2 to find the value of A: A + 3($0.64) = $3.34 A + $1.92 = $3.34 A ≈ $3.34 - $1.92 A ≈ $1.42

Therefore, the cost of one apple is approximately $1.42, and the cost of one pear is approximately $0.64.

Answer 2

$0.64

Explanation:

To find the cost of one apple and one pear, we can set up a system of equations based on the given information.

Let's use "A" to represent the cost of one apple and "P" to represent the cost of one pear.

From the first statement: "Five apples and six pears cost $10.94," we can write the equation:

5A + 6P = 10.94

From the second statement: "One apple and three pears cost $3.34," we can write the equation:

1A + 3P = 3.34

Now, we have a system of two equations:

5A + 6P = 10.94

1A + 3P = 3.34

We can use these equations to solve for the values of A and P. Let's use the elimination method. First, let's multiply equation (2) by 5 to make the coefficients of A in both equations equal:

5A + 6P = 10.94

5A + 15P = 16.70

Now, subtract equation (1) from equation (2) to eliminate A:

(5A + 15P) - (5A + 6P) = 16.70 - 10.94

This simplifies to:

9P = 5.76

Now, divide both sides by 9 to find the value of P:

P = 5.76 / 9

P ≈ $0.64 (rounded to the nearest cent)

Now that we know the cost of one pear (P), we can substitute it back into equation (2) to find the cost of one apple (A):

1A + 3(0.64) = 3.34

1A + 1.92 = 3.34

Subtract 1.92 from both sides:

1A = 3.34 - 1.92

1A ≈ $1.42 (rounded to the nearest cent)

So, the cost of one apple is approximately $1.42, and the cost of one pear is approximately $0.64.