Question

elva monitors her savings account online. on monday she withdraws money, and the change to account balance is -$51.25. on tuesday she deposits money and the change to her balance is she wants to know the total change in her account after the two transactions. write an expression for the total change in elvas account. -51.25 + 39.50 which amount is the best approximation of the total change in elvas account balance? -$20 -$90 -$80 -$10

Explanation:

Step1: Calculate the exact total change

The expression for total change is $-51.25 + 39.50$. Calculating this: $-51.25+39.50=-11.75$.

Step2: Approximate the result

Now, we approximate $-11.75$. Among the given options ($-\$20$, $-\$90$, $-\$80$, $-\$10$), $-11.75$ is closest to $-\$10$? Wait, no, wait. Wait, $-51.25$ is approximately $-50$ and $39.50$ is approximately $40$. So $-50 + 40=-10$. Wait, but the exact value is $-11.75$, which is closer to $-\$10$? Wait, no, wait, maybe I miscalculated. Wait, $-51.25 + 39.50 = -11.75$. So the best approximation among the options: $-\$10$ is the closest (since $-11.75$ is about $-10$ when approximated, as $-20$ is further, $-90$ and $-80$ are way off). Wait, but let's check again. The exact value is $-11.75$, which is approximately $-10$ (since $11.75$ is close to $10$ in absolute value, and the sign is negative). So the best approximation is $-\$10$? Wait, no, wait, maybe I made a mistake. Wait, $-51.25$ is a withdrawal (negative change), $39.50$ is a deposit (positive change). So total change is $-51.25 + 39.50 = -11.75$. Now, looking at the options: $-\$20$ is $-20$, which is $8.25$ away from $-11.75$; $-\$10$ is $1.75$ away. So yes, $-\$10$ is the best approximation. Wait, but the options are $-\$20$, $-\$90$, $-\$80$, $-\$10$. So the correct approximation is $-\$10$? Wait, but let's check the initial approximation. If we approximate $-51.25$ as $-50$ and $39.50$ as $40$, then $-50 + 40 = -10$, which matches the approximation of the exact value $-11.75$ being close to $-10$. So the best approximation is $-\$10$. Wait, but maybe I messed up. Wait, no, let's do the exact calculation: $-51.25 + 39.50 = -11.75$. So among the options, $-\$10$ is the closest (since $-11.75$ is $1.75$ away from $-10$, and $8.25$ away from $-20$, and way more from $-80$ and $-90$). So the best approximation is $-\$10$.

Wait, but wait, maybe the problem was that I misread the deposit amount? Wait, the original problem: "On Monday she withdraws money, and the change to account balance is $-\$51.25$. On Tuesday she deposits money and the change to her balance is [probably $+\$39.50$, since the expression is $-51.25 + 39.50$]. So the total change is $-51.25 + 39.50 = -11.75$, which is approximately $-\$10$. So the best approximation is $-\$10$.

Answer:

The best approximation of the total change in Elva’s account balance is $-\$10$.