To find the viable solution, we can set up an equation using the given information.
Let x be the number of chemistry sets and y be the number of robotics kits.
The cost of the chemistry sets is 8x, and the cost of the robotics kits is 10y.
Since Cindy spent her entire winnings of $50, the equation becomes:
8x + 10y = 50
To find the viable solution, we need to substitute the given options into this equation and see which one satisfies it.
Let's substitute (−5,9):
8(-5) + 10(9) = -40 + 90 = 50
Since the equation is satisfied, the viable solution is (−5,9). So, Cindy can purchase 9 robotics kits and -5 chemistry sets, which doesn't make sense in this context. Therefore, this option is not a valid solution.
Let's try substituting (5,1):
8(5) + 10(1) = 40 + 10 = 50
Again, the equation is satisfied, so the viable solution is (5,1). This means Cindy can purchase 1 robotics kit and 5 chemistry sets.
Let's try substituting (3,2.6):
8(3) + 10(2.6) = 24 + 26 = 50
The equation is satisfied, so the viable solution is (3,2.6). Cindy can purchase 2.6 robotics kits and 3 chemistry sets. However, since we can't purchase a fraction of a robotics kit, this option is not a valid solution.
Let's try substituting (0,5):
8(0) + 10(5) = 0 + 50 = 50
The equation is satisfied, so the viable solution is (0,5). Cindy can purchase 5 robotics kits and no chemistry set.
Based on the analysis, the viable solution is (5,1). Cindy can purchase 5 robotics kits and 1 chemistry set.
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 costs $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?(1 point) Responses (−5,9) left parenthesis negative 5 comma 9 right parenthesis (5,1) left parenthesis 5 comma 1 right parenthesis (3,2.6) left parenthesis 3 comma 2.6 right parenthesis (0,5)
1 answer
1 answer