Kate bought 3 pounds of rice and 1 pounds of beans for $4.50. Elise bought 4 pounds of rice and 2 pounds of beans for $7.00. What is the cost of a pound of rice? What is the cost of one pound of beans?
Well, it seems like Kate and Elise were having a little rice and bean competition! Let's figure out the cost of these tasty ingredients.
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!
Let's solve this problem step by step.
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.
To solve this problem, let's use a system of equations. Let's denote the cost of one pound of rice as 'r' and the cost of one pound of beans as 'b'.
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.
3r+1b = 4.50
4r+2b = 7.00
now solve as usual.