After spending 30% of his money, John had $140 left. How much did he have at first.
Siti and Ali saved $4500. Ali and Jim saved $2950. Siti saved thrice as much as Jim. How much did Ali save?
At a concert, there were 15 more children than adults. Each child paid $5 each and each adult paid $10 for a ticket. If the total amount of money collected from them was $150, how many children were there?
1. (1-.30)x = 140
3. C = A + 15
5C + 10A = 150
Substitute A+15 for C in second equation and solve for A. Insert that value into the first equation and solve for C. Check by inserting both values into the second equation.
To find the answer to the first question, we'll set up an equation.
Let's say John had x amount of money at first.
After spending 30% of his money, John had 100% - 30% = 70% of his money left.
We can express this as 70% of x, or 0.7x.
Given that John had $140 left, we can set up the equation:
0.7x = 140
To solve for x, we need to divide both sides of the equation by 0.7:
x = 140 / 0.7
x ≈ $200
Therefore, John had $200 at first.
To answer the second question, we can use a system of equations.
Let's assume Siti saved S dollars, Ali saved A dollars, and Jim saved J dollars.
Given that Siti saved thrice as much as Jim, we have the equation:
S = 3J
From the information provided, we know that Siti and Ali saved $4500 and Ali and Jim saved $2950. This gives us two equations:
S + A = 4500 (equation 1)
A + J = 2950 (equation 2)
Now we can substitute the value of S from equation 1 into equation 2:
3J + A = 4500 (equation 1, revised)
By subtracting equation 2 from this revised equation 1, we can eliminate A:
3J + A - A - J = 4500 - 2950
2J = 1550
J = 1550 / 2
J = $775
Therefore, Jim saved $775.
To find out how much Ali saved, we can substitute the value of J into equation 2:
A + 775 = 2950
A = 2950 - 775
A = $2175
Therefore, Ali saved $2175.
For the last question, we'll set up an equation based on the given information.
Let's assume the number of adults is A, and the number of children is C.
From the given information, we know that the number of children is 15 more than the number of adults, so we have:
C = A + 15 (equation 1)
The cost for each child's ticket is $5, and the cost for each adult's ticket is $10.
We can express the total amount of money collected from their ticket purchases as:
5C + 10A = 150 (equation 2)
Now we can substitute the value of C from equation 1 into equation 2:
5(A + 15) + 10A = 150
Simplifying the equation:
5A + 75 + 10A = 150
Combining like terms:
15A + 75 = 150
Subtracting 75 from both sides of the equation:
15A = 150 - 75
15A = 75
Dividing both sides by 15:
A = 75 / 15
A = 5
Therefore, there were 5 adults.
Now substituting this value of A into equation 1 to find the number of children:
C = 5 + 15
C = 20
Therefore, there were 20 children.