Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your an carlies stock rose by $1\frac{5}{8}$ points in trading today. let $y$ represent yesterdays stock pri i) what is a formula that correctly relates $y$ and $t$? ii) if yesterdays closing price was $32\frac{13}{16}$, what was todays closing price? - i) $t = y + 1\frac{5}{8}$ ii) todays closing price was $34\frac{7}{16}$. - i) $y = t + 1\frac{5}{8}$ ii) todays closing price was $33\frac{7}{16}$. - i) $y = t + 1\frac{5}{8}$ ii) todays closing price was $34\frac{7}{16}$. - i) $t = y + 1\frac{5}{8}$ ii) todays closing price was $33\frac{7}{16}$.

Explanation:

Part (i)

Step1: Analyze the relationship

The stock rose by \(1\frac{5}{8}\) points today. So today's price \(T\) is yesterday's price \(Y\) plus the rise. So the formula should be \(T = Y + 1\frac{5}{8}\).

Part (ii)

Step1: Convert mixed numbers

First, convert \(1\frac{5}{8}\) to sixteenths. \(1\frac{5}{8}=\frac{13}{8}=\frac{26}{16}\) and \(32\frac{13}{16}\) is the yesterday's price.

Step2: Add the prices

Now add \(32\frac{13}{16}\) and \(1\frac{5}{8}\) (which is \(\frac{26}{16}\) as a fraction part).
First, add the whole numbers: \(32 + 1=33\).
Then add the fractions: \(\frac{13}{16}+\frac{26}{16}=\frac{39}{16}=2\frac{7}{16}\).
Now add the whole number results: \(33 + 2\frac{7}{16}=34\frac{7}{16}\)? Wait, no, wait. Wait, \(1\frac{5}{8}\) is \(1 + \frac{5}{8}\). So \(32\frac{13}{16}+1\frac{5}{8}\). Let's do it correctly.
\(32\frac{13}{16}+1\frac{5}{8}=32\frac{13}{16}+1\frac{10}{16}=(32 + 1)+(\frac{13}{16}+\frac{10}{16})=33+\frac{23}{16}=33 + 1\frac{7}{16}=34\frac{7}{16}\)? Wait, no, \(\frac{23}{16}=1\frac{7}{16}\), so \(33+1\frac{7}{16}=34\frac{7}{16}\). But wait, let's check the options. Wait, maybe I made a mistake. Wait, \(1\frac{5}{8}\) is \(1.625\) and \(32\frac{13}{16}=32.8125\). Adding them: \(32.8125 + 1.625 = 34.4375\). Now, \(34\frac{7}{16}=34.4375\) (since \(\frac{7}{16}=0.4375\)). And \(33\frac{7}{16}=33.4375\). Wait, but according to the formula \(T = Y+1\frac{5}{8}\), so \(Y = 32\frac{13}{16}\), \(T=32\frac{13}{16}+1\frac{5}{8}\). Let's compute the fraction part: \(\frac{13}{16}+\frac{5}{8}=\frac{13}{16}+\frac{10}{16}=\frac{23}{16}=1\frac{7}{16}\). Then the whole number part: \(32 + 1+1=34\) (wait, \(32 + 1\) from the \(1\frac{5}{8}\) whole number, plus the \(1\) from the fraction addition). So \(34\frac{7}{16}\). But let's check the options. The first option has (i) \(T = Y + 1\frac{5}{8}\) and (ii) \(34\frac{7}{16}\), but wait, no, wait the last option? Wait, no, let's re - check. Wait, maybe I messed up the whole number addition. Wait, \(32\frac{13}{16}+1\frac{5}{8}\): \(32 + 1=33\), \(\frac{13}{16}+\frac{10}{16}=\frac{23}{16}=1\frac{7}{16}\), so \(33 + 1\frac{7}{16}=34\frac{7}{16}\). But looking at the options, the first option group: (i) \(T = Y+1\frac{5}{8}\), (ii) \(34\frac{7}{16}\). But wait, the last option group: (i) \(T = Y + 1\frac{5}{8}\), (ii) \(33\frac{7}{16}\) is wrong. Wait, maybe the question has a typo, but according to the formula \(T = Y + 1\frac{5}{8}\), and the calculation, the correct (i) is \(T = Y+1\frac{5}{8}\), and (ii) is \(34\frac{7}{16}\). But looking at the options, the first option is:

i) \(T = Y + 1\frac{5}{8}\)

ii) Today's closing price was \(34\frac{7}{16}\).

Wait, but let's check again. \(32\frac{13}{16}+1\frac{5}{8}\). \(1\frac{5}{8}=\frac{13}{8}=\frac{26}{16}\). \(32\frac{13}{16}+\frac{26}{16}=32+\frac{13 + 26}{16}=32+\frac{39}{16}=32 + 2\frac{7}{16}=34\frac{7}{16}\). Yes. So the correct option is the first one:

Answer:

i) \(T = Y + 1\frac{5}{8}\)

ii) Today's closing price was \(34\frac{7}{16}\) (the first option group: i) \(T = Y + 1\frac{5}{8}\), ii) Today's closing price was \(34\frac{7}{16}\))