Final answer:
By setting up a system of equations and solving for two unknowns, we find that the math club purchased 11 Super X calculators and 5 Super ZX calculators.
Step-by-step explanation:
To solve how many Super X and Super ZX calculators were purchased, we set up a system of equations. Let x be the number of Super X calculators and y be the number of Super ZX calculators.
The first equation represents the total number of calculators: x + y = 16.
The second equation represents the total cost: 40x + 65y = 765.
Solving the system of equations:
- Subtract the first equation from the second equation, multiplied by 40: 40y = 765 - 640, which simplifies to 40y = 125.
- Divide by 40 to find y: y = 125/40, which simplifies to y = 3.125. Since we can't have a fraction of a calculator, we review our steps for any errors.
- By reviewing our calculations, we realize that the correct subtraction should yield 40x + 65y = 765 minus 40x + 40y = 640 (which is 40 times the first equation), giving us 25y = 125.
- Now we divide by 25 to find y: y = 125/25, which results in y = 5. So there are 5 Super ZX calculators.
- Substitute y = 5 back into the first equation: x + 5 = 16 to find x.
- Solving for x gives us x = 16 - 5, which simplifies to x = 11. Therefore, there are 11 Super X calculators.
The math club purchased 11 Super X calculators and 5 Super ZX calculators.