Question

if you bought 20 pieces of cake from two varieties one of them cost 12 and the other costs 20 and the total is 360 how many pieces of cake did you buy from each variety?

Answer 1

By setting up a system of equations with one equation for the total number of cakes and another for the total cost, and then solving it, we find that 5 pieces of the first variety (at $12 each) and 15 pieces of the second variety (at $20 each) were bought.

Step-by-step explanation:

To solve the problem of determining how many pieces of each variety of cake were bought, we can use a system of equations. Let's denote the number of variety 1 cakes, which cost $12 each, as x, and the number of variety 2 cakes, which cost $20 each, as y.

The first equation comes from the total number of cakes bought: x + y = 20. The second equation comes from the total cost of the cakes: 12x + 20y = 360.

Now we can solve this system of equations step-by-step:

• Multiply the first equation by 12: 12x + 12y = 240.
• Subtract this new equation from the second equation to eliminate x: (12x + 20y) - (12x + 12y) = 360 - 240.
• Simplify to find y: 8y = 120.
• Divide by 8 to find y: y = 15. This means 15 pieces of the second variety were bought.
• Substitute y = 15 back into the first equation to find x: x + 15 = 20.
• Solve for x: x = 5. This means 5 pieces of the first variety were bought.

Thus, 5 pieces of the $12 variety and 15 pieces of the $20 variety were bought to make a total of 20 pieces for $360.