ISEE Upper Level Mathematics Achievement Question of the Day

1. $2$
2. $5$ (correct answer)
3. $8$
4. $11$

Explanation: This question tests your ability to substitute known values into a linear equation and solve for an unknown coefficient. When you see an equation with multiple variables and are given specific values that make the equation true, you need to substitute those values and work backwards to find the missing piece. Since we know that $x = 4$ is the solution when $a = 3$ and $c = 17$, we can substitute these values directly into the equation $ax + b = c$. This gives us: $3(4) + b = 17$. Simplifying the left side: $12 + b = 17$. To solve for $b$, subtract 12 from both sides: $b = 17 - 12 = 5$. Let's examine why the other answers are incorrect. Choice A ($b = 2$) would give us $3(4) + 2 = 14$, which doesn't equal 17. Choice C ($b = 8$) would result in $3(4) + 8 = 20$, which is too large. Choice D ($b = 11$) would produce $3(4) + 11 = 23$, which is much too large. Only choice B ($b = 5$) satisfies our equation: $3(4) + 5 = 12 + 5 = 17$ ✓ When working with linear equations containing multiple parameters, always substitute the known values first, then solve for the unknown. Double-check your answer by plugging it back into the original equation to verify that both sides are equal.