Question

the average reading score on certain tests is given by $y = 0.153x + 255.33$, where $x$ is the number of years past 1970. in what year would the average reading score be 259.002 if this model is accurate?
the average reading score would be 259.002 in \square. (type a whole number.)

Explanation:

Step1: Substitute y into the equation

Set $y=259.002$ in $y=0.153x+255.33$, so:
$$259.002 = 0.153x + 255.33$$

Step2: Isolate the term with x

Subtract 255.33 from both sides:
$$259.002 - 255.33 = 0.153x$$
$$3.672 = 0.153x$$

Step3: Solve for x

Divide both sides by 0.153:
$$x = \frac{3.672}{0.153}$$
$$x = 24$$

Step4: Calculate the target year

Add x to 1970:
$$1970 + 24 = 1994$$

Answer:

1994