19. ( 3 + (-14) ) 20. ( -27 + (-3) ) 21. ( 8 - (-15) ) 22. ( -9 + (-19) ) 23. ( -13 - (-20) ) 24. ( -20 + (-2) ) directions: read each problem carefully, then find the sum or difference. 25. on the first play of a game, the eagles running back lost three yards. on their next play, the quarterback was sacked for a loss of fourteen yards. find the total yards in these two plays. 26. brett and max are diving. brett is 34 feet below the surface and max is 25 feet below the surface. how many feet above brett is max? 27. once a hot - air balloon reached its highest point, it dropped 25 feet. then five minutes later, it dropped another 13 feet. find its total change in altitude during this time. 28. at sunset, the temperature was 4 degrees. then at sunrise the next morning, it was - 7 degrees. what is the difference between these temperatures? 29. the golfer with the highest score in a tournament was nine over par. the golfer with the lowest score was five below par. what was the range in golf scores? 30. nick’s bank account balance was $21. if he writes a check for $30 and his bank charges him $35 for overdrawing his account, find his account balance. © gina wilson (all things algebra®), llc 2017

Question

19. ( 3 + (-14) )  20. ( -27 + (-3) )  21. ( 8 - (-15) )  22. ( -9 + (-19) )  23. ( -13 - (-20) )  24. ( -20 + (-2) )  directions: read each problem carefully, then find the sum or difference.  25. on the first play of a game, the eagles running back lost three yards. on their next play, the quarterback was sacked for a loss of fourteen yards. find the total yards in these two plays.  26. brett and max are diving. brett is 34 feet below the surface and max is 25 feet below the surface. how many feet above brett is max?  27. once a hot - air balloon reached its highest point, it dropped 25 feet. then five minutes later, it dropped another 13 feet. find its total change in altitude during this time.  28. at sunset, the temperature was 4 degrees. then at sunrise the next morning, it was - 7 degrees. what is the difference between these temperatures?  29. the golfer with the highest score in a tournament was nine over par. the golfer with the lowest score was five below par. what was the range in golf scores?  30. nick’s bank account balance was $21. if he writes a check for $30 and his bank charges him $35 for overdrawing his account, find his account balance.  © gina wilson (all things algebra®), llc 2017

Accepted Answer

### Problem 19: $ 3 + (-14) $
# Explanation:
## Step 1: Understand the operation
Adding a negative number is like subtracting its absolute value. So $ 3 + (-14) = 3 - 14 $.
## Step 2: Perform the subtraction
$ 3 - 14 = -11 $.
# Answer: $ -11 $

### Problem 20: $ -27 + (-3) $
# Explanation:
## Step 1: Add the absolute values
When adding two negative numbers, we add their absolute values and keep the negative sign. So $ |-27| + |-3| = 27 + 3 = 30 $.
## Step 2: Apply the negative sign
Since both numbers are negative, the result is $ -30 $.
# Answer: $ -30 $

### Problem 21: $ 8 - (-15) $
# Explanation:
## Step 1: Subtracting a negative is adding the positive
Subtracting a negative number is equivalent to adding its positive counterpart. So $ 8 - (-15) = 8 + 15 $.
## Step 2: Perform the addition
$ 8 + 15 = 23 $.
# Answer: $ 23 $

### Problem 22: $ -9 + (-19) $
# Explanation:
## Step 1: Add the absolute values
For two negative numbers, add their absolute values. $ |-9| + |-19| = 9 + 19 = 28 $.
## Step 2: Apply the negative sign
The result is $ -28 $.
# Answer: $ -28 $

### Problem 23: $ -13 - (-20) $
# Explanation:
## Step 1: Subtracting a negative is adding the positive
$ -13 - (-20) = -13 + 20 $.
## Step 2: Perform the addition
$ -13 + 20 = 7 $ (because $ 20 - 13 = 7 $).
# Answer: $ 7 $

### Problem 24: $ -20 + (-2) $
# Explanation:
## Step 1: Add the absolute values
Adding two negative numbers: $ |-20| + |-2| = 20 + 2 = 22 $.
## Step 2: Apply the negative sign
Result is $ -22 $.
# Answer: $ -22 $

### Problem 25: Total yards lost
# Explanation:
## Step 1: Represent the losses as negative numbers
First play: lost 3 yards, so $ -3 $. Second play: lost 14 yards, so $ -14 $.
## Step 2: Find the total
Total yards lost is $ -3 + (-14) $. Adding two negatives: $ |-3| + |-14| = 3 + 14 = 17 $, so result is $ -17 $ (total loss of 17 yards).
# Answer: $ -17 $ (or 17 yards lost)

### Problem 26: How many feet above Brett is Max?
# Explanation:
## Step 1: Represent their depths
Brett: 34 feet below, so $ -34 $ (or just 34 as depth). Max: 25 feet below, so $ -25 $ (or 25 as depth).
## Step 2: Find the difference
To find how much above Brett Max is, calculate $ 34 - 25 = 9 $ (since Max is shallower, the difference is positive).
# Answer: $ 9 $ feet

### Problem 27: Total change in altitude
# Explanation:
## Step 1: Represent the drops as negative changes
First drop: 25 feet, so $ -25 $. Second drop: 13 feet, so $ -13 $.
## Step 2: Find the total change
Total change is $ -25 + (-13) $. Adding the absolute values: $ 25 + 13 = 38 $, so total change is $ -38 $ feet (38 feet drop).
# Answer: $ -38 $ feet (or 38 feet drop)

### Problem 28: Temperature difference
# Explanation:
## Step 1: Identify the temperatures
Sunset: $ 4^\circ $. Sunrise: $ -7^\circ $.
## Step 2: Calculate the difference
Difference is $ 4 - (-7) = 4 + 7 = 11 $ degrees.
# Answer: $ 11 $ degrees

### Problem 29: Range in golf scores
# Explanation:
## Step 1: Represent the scores
Highest: 9 over par, so $ +9 $. Lowest: 5 below par, so $ -5 $.
## Step 2: Calculate the range
Range is highest - lowest: $ 9 - (-5) = 9 + 5 = 14 $.
# Answer: $ 14 $

### Problem 30: Account balance
# Explanation:
## Step 1: Initial balance and transactions
Initial balance: $ \$21 $. Writes a check for $ \$30 $: $ 21 - 30 = -9 $. Then bank charges $ \$35 $: $ -9 - 35 = -44 $.
## Step 2: Final balance
Final balance is $ -44 $ dollars (or $ \$ -44 $).
# Answer: $ -44 $ dollars (or $ \$ -44 $)

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 19: \( 3 + (-14) \)

Step 1: Understand the operation

Step 2: Perform the subtraction

Step 1: Add the absolute values

Step 2: Apply the negative sign

Step 1: Subtracting a negative is adding the positive

Step 2: Perform the addition

Answer:

Problem 20: \( -27 + (-3) \)