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)