[Solved] If 4 apples and 6 bananas cost $1.56, and 9 apples and 7 bananas cost $2.60, what is the cost of one apple and one banana?

Question: If 4 apples and 6 bananas cost $1.56, and 9 apples and 7 bananas cost $2.60. What are the cost of one apple and one banana?

We will solve the system of linear equations using the elimination method.

Step 1: Set up the equations

We are given the following information:

• 4 apples and 6 bananas cost $1.56
• 9 apples and 7 bananas cost $2.60

Let x be the cost of one apple, and y be the cost of one banana.

We can create the following system of linear equations:

1. 4x + 6y = 1.56
2. 9x + 7y = 2.60

Step 2: Eliminate one variable.

We’ll eliminate y by multiplying both equations by necessary multiples so that the coefficients of y in both equations are the same.

Multiply equation (1) by 7 and equation (2) by 6:

7(4x + 6y) = 7(1.56) 6(9x + 7y) = 6(2.60)

Which results in:

28x + 42y = 10.92 54x + 42y = 15.60

Step 3: Solve for x

Subtract equation (1) from equation (2) to eliminate the y variable:

54x + 42y – (28x + 42y) = 15.60 – 10.92 26x = 4.68

Now, divide by 26 to find the value of x:

x = 4.68 / 26 x ≈ 0.18

Step 4: Solve for y

Now that we have the value of x, we can find the value of y by plugging x back into either equation (1) or (2). We will use equation (1):

4x + 6y = 1.56 4(0.18) + 6y = 1.56 0.72 + 6y = 1.56

Subtract 0.72 from both sides:

6y = 0.84

Divide by 6 to find the value of y:

y ≈ 0.14

Step 5: Interpret the results

The cost of one apple (x) is approximately $0.18, and the cost of one banana (y) is approximately $0.14.

Method 2

Solution: From the information given, we will form an equation.

We will convert the price to cents; it will make calculations easier.

The cost of 4 apples and 6 bananas cost $1.56=156 ¢

Cost of 9 apples and 7 bananas $2.60=260 ¢

Let a represent the number of apples.

Let b represent the number of bananas.

According to the question, 4 apples and 6 bananas cost a total of $1.56, and 9 apples and 7 bananas cost a total of $2.60

Now, we will combine these equations in such a way that it eliminates either a or b.

There are multiple ways of doing this; we will use the elimination method.

We will choose to first multiply equation 1 by 9 and equation 2 by 4; we get

9(4a + 6b = 156)

4(9a + 7b = 260)

Subtracting equation 4 from 3, we get

Dividing both sides of equation 5 by 26, we get

∴ Value of b = 14

Substituting the value of b in equation 1, we get

4a + 6(14) = 156

4a + 84 = 156

4a = 156 – 84

4a = 72

a = 18

∴Value of a = 18

Hence, the cost of an apple is 18¢ or $0.18, and the cost of a banana is 14¢ or $0.14

Conclusion

If 4 apples and 6 bananas cost $1.56, 9 apples and 7 bananas cost $2.60. The cost of an apple is $0.18, and the cost of a banana is $0.14