Question

7.ns.a.1d
about this standard
apply properties of
operations as strategies to
add and subtract rational
numbers.
account cenamalone
58
$7
balance
gained
$14
we have
gold
hammer
wrench $-8
$-7
$28
two ounces
gold
horse
back
$-22
$7
11.2
gold
interest
$-16
= $-3
is mr. skinner swindling malone?
yes no
if yes, what is miss malone’s actual account balance?

Explanation:

Step1: List all transactions

The transactions are: \( +\$7 \), \( +\$74 \), \( -\$8 \), \( -\$7 \), \( +\$28 \), \( -\$22 \), \( +\$7 \), \( -\$76 \)

Step2: Sum positive transactions

Positive amounts: \( 7 + 74 + 28 + 7 = 116 \)

Step3: Sum negative transactions

Negative amounts (absolute values): \( 8 + 7 + 22 + 76 = 113 \)

Step4: Calculate net balance

Net balance: \( 116 - 113 = 3 \)? Wait, no, let's add all with signs:
\( 7 + 74 - 8 - 7 + 28 - 22 + 7 - 76 \)
Group positives and negatives:
\( (7 + 74 + 28 + 7) + (-8 - 7 - 22 - 76) \)
\( 116 + (-113) = 3 \)? But the given result is \( -\$3 \). Wait, maybe I misread signs. Wait the last line says \( =\$-3 \), but let's recalculate:

Wait let's do step by step:
Start with 0 (assuming initial balance? Wait no, maybe the first "balance forward" is some, but the transactions are as listed. Wait the transactions are:

\( +7 \) (credit), \( +74 \) (credit), \( -8 \) (debit), \( -7 \) (debit), \( +28 \) (credit), \( -22 \) (debit), \( +7 \) (credit), \( -76 \) (debit)

Now sum all:

\( 7 + 74 = 81 \)

\( 81 - 8 = 73 \)

\( 73 - 7 = 66 \)

\( 66 + 28 = 94 \)

\( 94 - 22 = 72 \)

\( 72 + 7 = 79 \)

\( 79 - 76 = 3 \)

So the actual balance should be \( +\$3 \), but the given result is \( -\$3 \). So the calculated balance is \( \$3 \), but the provided result is \( -\$3 \), so there's a mistake. So Mr. Skinner's calculation is wrong (he got \( -\$3 \), but actual is \( +\$3 \)? Wait no, wait maybe the initial balance? Wait the first line says "balance forward" but maybe the transactions are the ones listed. Wait the final result given is \( -\$3 \), but our calculation is \( +\$3 \). Wait no, let's check again:

Wait the transactions:

\( +7 \), \( +74 \), \( -8 \), \( -7 \), \( +28 \), \( -22 \), \( +7 \), \( -76 \)

Let's add them in order:

\( 7 + 74 = 81 \)

\( 81 - 8 = 73 \)

\( 73 - 7 = 66 \)

\( 66 + 28 = 94 \)

\( 94 - 22 = 72 \)

\( 72 + 7 = 79 \)

\( 79 - 76 = 3 \)

So the actual balance is \( \$3 \), but the recorded is \( -\$3 \). So Mr. Skinner is swindling (since he shows negative instead of positive). So YES, and the actual balance is \( \$3 \). Wait but the problem says "Miss Malone’s actual account balance". Wait maybe I made a sign error. Wait let's check the transactions again. The last transaction is \( -\$76 \), others:

Wait the transactions are:

Credit: \( +7, +74, +28, +7 \) (total 7+74=81, +28=109, +7=116)

Debit: \( -8, -7, -22, -76 \) (total -8-7=-15, -22=-37, -76=-113)

116 - 113 = 3. So actual balance is \( \$3 \), but the result is \( -\$3 \). So he is swindling (YES), and actual balance is \( \$3 \).

Answer:

YES, Miss Malone’s actual account balance is \$3.