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Pick one of the answer for each of the questions

Adam has $2 and is saving $2 each day. Brodie has $8 and is spending $1 each day After how many days will each person have the same amount of money? *
15 points
A. 5x + 4 = 3x - 2
B. 3x + 6 = -2x + 1
C. 2x + 2 = -x + 8
D. x + 8 = 2x + 7

2. A number increased by 8 is equal to twice the same number increased by 7. *
15 points
A. 5x + 4 = 3x - 2
B. 3x + 6 = -2x + 1
C. 2x + 2 = -x + 8
D. x + 8 = 2x + 7

3. Spot weighs 6 pounds and gains one pound each week. Buddy weighs 2 pounds and gains 2 pounds each week. After how many weeks will the puppies weigh the same? *
15 points
A. x + 6 = 2x + 2
B. 3x + 6 = -2x + 1
C. 2x + 2 = -x + 8
D. x + 8 = 2x + 7

4. Five less than two times a number is equal to 4 less than the same number. *
15 points
A. x + 6 = 2x + 2
B. 2x - 5 = x - 4
C. 2x + 2 = -x + 8
D. x + 8 = 2x + 7

5. Ann has an empty cup and adds 1 ounce of water per second. Bob has 12 ounces of water and drinks 2 ounces per second. After how many seconds will they have the same amount of water? *
20 points
A. -2x + 12 = -x + 6
B. 2x - 5 = x - 4
C. 2x + 2 = -x + 8
D. x = -2x + 12

6. Tom has 12 candies and eats 2 each minute. Sue has 6 candies and eats 1 every minute. After how many minutes will they have the same number of candies? *
20 points
A. -2x + 12 = -x + 6
B. 2x - 5 = x - 4
C. 2x + 2 = -x + 8
D. x = -2x + 12

User Snagnever
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7.8k points

1 Answer

1 vote

Answer:

Explanation:

Let's solve each problem one by one:

1. Adam has $2 and is saving $2 each day. Brodie has $8 and is spending $1 each day. After how many days will each person have the same amount of money?

Let's assume the number of days is represented by 'x'.

Adam's money after 'x' days = $2 + $2x

Brodie's money after 'x' days = $8 - $1x

To find the number of days when they have the same amount of money, we set up an equation:

$2 + $2x = $8 - $1x

Simplifying the equation:

$2x + $1x = $8 - $2

$3x = $6

x = $6 / $3

x = 2

Therefore, after 2 days, Adam and Brodie will have the same amount of money.

Answer: A. 5x + 4 = 3x - 2 (incorrect)

2. A number increased by 8 is equal to twice the same number increased by 7.

Let's represent the number by 'x'.

Equation: x + 8 = 2x + 7

Solving the equation:

x - 2x = 7 - 8

-x = -1

x = 1

Therefore, the number is 1.

Answer: D. x + 8 = 2x + 7 (correct)

3. Spot weighs 6 pounds and gains one pound each week. Buddy weighs 2 pounds and gains 2 pounds each week. After how many weeks will the puppies weigh the same?

Let's represent the number of weeks by 'x'.

Spot's weight after 'x' weeks = 6 + 1x

Buddy's weight after 'x' weeks = 2 + 2x

To find the number of weeks when they weigh the same, we set up an equation:

6 + 1x = 2 + 2x

Simplifying the equation:

x - 2x = 2 - 6

-x = -4

x = 4

Therefore, after 4 weeks, Spot and Buddy will weigh the same.

Answer: A. x + 6 = 2x + 2 (incorrect)

4. Five less than two times a number is equal to 4 less than the same number.

Let's represent the number by 'x'.

Equation: 2x - 5 = x - 4

Solving the equation:

2x - x = -4 + 5

x = 1

Therefore, the number is 1.

Answer: B. 2x - 5 = x - 4 (correct)

5. Ann has an empty cup and adds 1 ounce of water per second. Bob has 12 ounces of water and drinks 2 ounces per second. After how many seconds will they have the same amount of water?

Let's represent the number of seconds by 'x'.

Ann's water after 'x' seconds = 1x ounces

Bob's water after 'x' seconds = 12 - 2x ounces

To find the number of seconds when they have the same amount of water, we set up an equation:

1x = 12 - 2x

Simplifying the equation:

1x + 2x = 12

3x = 12

x = 12 / 3

x = 4

Therefore, after 4 seconds, Ann and Bob will have the same amount of water.

Answer: A. -2x + 12 = -x + 6 (incorrect)

6. Tom has

12 candies and eats 2 each minute. Sue has 6 candies and eats 1 every minute. After how many minutes will they have the same number of candies?

Let's represent the number of minutes by 'x'.

Tom's candies after 'x' minutes = 12 - 2x

Sue's candies after 'x' minutes = 6 - 1x

To find the number of minutes when they have the same number of candies, we set up an equation:

12 - 2x = 6 - 1x

Simplifying the equation:

-2x + 1x = 6 - 12

-x = -6

x = 6

Therefore, after 6 minutes, Tom and Sue will have the same number of candies.

Answer: A. -2x + 12 = -x + 6 (correct)

User Tarick Welling
by
8.6k points