Step-by-step explanation
1.
Given:
Let x and y = two numbers
x + y = 45 -> Equation 1
x = 2y (one number is TWICE as large as the second number) -> Equation 2
Solution:
x + y = 45
We substitute x from the second equation to the first equation:
[@x = 2y]
2y + y = 45
3y = 45
y = 45/3
y = 15
Then, we solve for x by substituting the value of y above to the second equation:
x = 2(15)
x = 30
Answer: The numbers are 15 and 30.
2.
Given:
Total Number of Fruits = 16
Let
M =number of Maria's fruits
J =number of Jack's fruits
P =number of Paul's fruits
M = 3J + 3 (three more than thrice fruits as Jack) -> Equation 1
P = 3J - 1 (one less than thrice fruits as jack) -> Equation 2
M + P + J = 16 -> Equation 3
Solution:
We substitute equations 1 and 2 to equation 3:
(3J + 3) + (3J - 1) + J = 16
3J + 3 + 3J - 1 + J = 16
7J + 2 = 16
7J = 16 - 2
7J = 14
J = 14/7
J = 2 fruits
Then, we substitute the value of J we obtained from above to equations 1 and 2:
Equation 1:
M = 3J + 3
[@ J = 2]
M = 3(2) + 3
M = 6 + 3
M = 9 fruits
Equation 2:
P = 3J - 1
[@ J = 2]
P = 3(2) - 1
P = 6 - 1
P = 5 fruits
Answer:
- Jack has 2 fruits
- Mary has 9 fruits
- Paul has 5 fruits
3.
Given:
Depth of Well = 30 ft
Let x = number of days
Jump Length = 3x feet
Fall Length = - 2x feet
Solution:
We just add the Jump length to the fall length and equate their sum to 30 ft:
Jump Length + Fall Length = 30 ft
3x + (-2x) = 30
Answer: x = 30 days
4.
Yes, we just need a 3-digit 8 added to a 2-digit 8 and three one-digit 8s:
888 + 88 + 8 + 8 + 8 = 1000
PH
