Question 19·50 Super-Hard SAT Problem Solving and Data Analysis Questions·Problem Solving and Data Analysis

Type $f(x)=0.75x-6$, then $f(0)$. Desmos shows $-6$, so the old line contains $(0,-6)$. Even if $0$ is outside the data’s temperature range, this is an algebraic check of the line, not a prediction of sales.

Use the given Fahrenheit conversion. Type $g(x)=1.8x+32$, then $g(0)$. Desmos shows $32$, so the point’s new temperature coordinate is $F=32$.

The old $y$ counts hundreds of smoothies, so multiply it by $100$ to get individual smoothies. Type $h(x)=100f(x)$, then $h(0)$. Desmos shows $-600$, making the converted algebraic point $(F,N)=(32,-600)$. The negative value is not a real sales count.

Type the left side with $N=-600$, then each choice’s right side with $F=32$. Desmos shows $-1800$ on the left; the right sides, in order, are $-1800$, $2200$, $600$, and $1400$. Only $3N=125F-5800$ contains the converted point, so it gives the same line in Fahrenheit and individual smoothies. Choice A.

The model uses Celsius, so solve the Fahrenheit equation for the old input $x$. Subtract $32$:

Divide by $1.8$:

Put that expression wherever the old model has $x$. The output is still $y$, measured in hundreds of smoothies:

Since $N=100y$, multiply the whole predicted output by $100$, not only its constant term:

Distribute $100$:

Type $\frac{100(0.75)}{1.8}$ in Desmos. It shows $41.666\ldots$; the fraction button gives $\frac{125}{3}$. So the rewritten output is:

Multiply by $3$ to match the choices:

Distribute $125$:

Combine the constants: $3N=125F-5800$. This is the same fitted line in the new units. Choice A.