Cindy won 50.00 for getting first place in the science fair. She spent her winnings on robotics kits and chemistry sets. Each robotics kit y costs 10.00, while each chemistry set cost 8.00 x. Which of the following is a viable solution to the number of robotics kits and chemistry sets Cindy can purchase, assuming she spends her entire winnings?
To find the viable solution for the number of robotics kits and chemistry sets Cindy can purchase, we need to take into account the cost of each item.
Let's assume Cindy buys y robotics kits and x chemistry sets. The cost of each robotics kit is $10.00, and the cost of each chemistry set is $8.00.
The total cost of the robotics kits is 10.00 * y.
The total cost of the chemistry sets is 8.00 * x.
Since Cindy spent her entire winnings of $50.00, we can set up the equation:
10.00y + 8.00x = 50.00
To find a viable solution, we need to find integer values for y and x that satisfy this equation.
By trial and error, we can find one possible solution:
If y = 5 and x = 2, then:
10.00 * 5 + 8.00 * 2 = 50.00
Therefore, one viable solution is that Cindy can purchase 5 robotics kits and 2 chemistry sets with her entire winnings.
Let's assume Cindy buys "y" robotics kits and "x" chemistry sets.
The cost of each robotics kit is $10.00, so the total cost of the robotics kits is y * $10.
The cost of each chemistry set is $8.00, so the total cost of the chemistry sets is x * $8.
Since Cindy spent her entire winnings of $50, we can write the equation:
y * $10 + x * $8 = $50
To find a viable solution, we can substitute different values for y and x until we find a combination that satisfies the equation. Here are a few possible solutions:
1. y = 3, x = 2
In this case, 3 robotics kits cost $30 (3 * $10), and 2 chemistry sets cost $16 (2 * $8). The total cost is $30 + $16 = $46.
2. y = 1, x = 5
In this case, 1 robotics kit costs $10 (1 * $10), and 5 chemistry sets cost $40 (5 * $8). The total cost is $10 + $40 = $50.
3. y = 2, x = 4
In this case, 2 robotics kits cost $20 (2 * $10), and 4 chemistry sets cost $32 (4 * $8). The total cost is $20 + $32 = $52, which exceeds Cindy's winnings of $50, so it is not a viable solution.
Therefore, a viable solution is y = 1 (1 robotics kit) and x = 5 (5 chemistry sets). Cindy can purchase 1 robotics kit and 5 chemistry sets using her entire winnings.
To find a viable solution to the number of robotics kits and chemistry sets Cindy can purchase, we need to consider that she won $50.00 and wants to spend her entire winnings.
Let's assume that Cindy buys y robotics kits and x chemistry sets.
The cost of each robotics kit is $10.00, so the total cost of y robotics kits would be 10y.
The cost of each chemistry set is $8.00, so the total cost of x chemistry sets would be 8x.
Since Cindy wants to spend her entire winnings of $50.00, we can set up the following equation:
10y + 8x = 50
We can solve this equation to find the viable solutions for y and x, which represent the number of robotics kits and chemistry sets, respectively.
There are multiple solutions for y and x that satisfy this equation. One possible solution is:
y = 2 (Cindy buys 2 robotics kits)
x = 3 (Cindy buys 3 chemistry sets)
With this solution, the total cost of the robotics kits would be 10 * 2 = $20.00, and the total cost of the chemistry sets would be 8 * 3 = $24.00. The sum of these costs is indeed $50.00, which means Cindy can purchase 2 robotics kits and 3 chemistry sets while spending her entire winnings.