3r+1b = 4.50
4r+2b = 7.00
now solve as usual.
4r+2b = 7.00
now solve as usual.
We'll start by considering the cost of rice. Kate bought 3 pounds of rice for $4.50, so the cost of one pound of rice is $4.50 divided by 3, which is $1.50. Voila!
Now let's move on to the beans. Elise bought 2 pounds of beans for $7.00. To find the cost of one pound of beans, we divide $7.00 by 2, and we get $3.50. Easy peasy!
So, the cost of one pound of rice is $1.50, and the cost of one pound of beans is $3.50. Enjoy your delicious mathematics meal!
Step 1: Assign variables.
Let's assign:
- r = cost of 1 pound of rice
- b = cost of 1 pound of beans
Step 2: Write the equations based on the given information.
Based on the information given, Kate bought 3 pounds of rice and 1 pound of beans for $4.50, and Elise bought 4 pounds of rice and 2 pounds of beans for $7.00. This can be expressed in two equations:
3r + b = 4.50 Equation 1
4r + 2b = 7.00 Equation 2
Step 3: Solve the system of equations.
We will use the elimination method to solve the system of equations. Let's multiply Equation 1 by -2 to cancel out the "b" terms:
-6r - 2b = -9.00 (multiply Equation 1 by -2)
4r + 2b = 7.00 (Equation 2)
Adding the two equations together eliminates the "b" terms:
-6r + 4r - 2b + 2b = -9.00 + 7.00
Simplifying, we have:
-2r = -2.00
Dividing both sides of the equation by -2, we find:
r = 1.00
Step 4: Substitute the value of r back into Equation 1 to find b.
Using Equation 1:
3r + b = 4.50
Substituting r = 1.00:
3(1) + b = 4.50
Simplifying, we have:
3 + b = 4.50
Subtracting 3 from both sides of the equation:
b = 4.50 - 3
Simplifying:
b = 1.50
Step 5: Answer the question.
The cost of one pound of rice (r) is $1.00, and the cost of one pound of beans (b) is $1.50.
From the information given, we can write the following equations:
Equation 1: 3r + 1b = 4.50
Equation 2: 4r + 2b = 7.00
We will solve this system of equations to find the values of 'r' and 'b'.
To eliminate the variables 'b', let's multiply Equation 1 by 2 and Equation 2 by -1:
Equation 3: 6r + 2b = 9.00 (2 * Equation 1)
Equation 4: -4r - 2b = -7.00 (-1 * Equation 2)
Adding Equation 3 and Equation 4, the 'b' terms cancel out:
6r - 4r + 2b - 2b = 9.00 - 7.00
2r = 2.00
Dividing both sides by 2, we get:
r = 1.00
Therefore, the cost of one pound of rice is $1.00.
To find the cost of one pound of beans, substitute the value of 'r' into Equation 1:
3(1.00) + 1b = 4.50
3.00 + 1b = 4.50
1b = 4.50 - 3.00
1b = 1.50
Therefore, the cost of one pound of beans is $1.50.