1/) Joe and Jerry went for a bike trek during nthe holidays. On the first day they rode 1/3 of the total distance. On the second day they were tired and only rode 1/4 of the remaining distance. On the third day they rode half of the distance left. The last day they rode the remaining 18 km. How far did they ride together?
2.) George has three as many marbles as Sam. If George gives 5 of his marbles to Sam, George will have twice as many marbles as Sam. How many marbles does Sam have?
3rd and 4th days ... 18 km + 18 km = 36 km
36 km = 3/4 d after 1st day ... d = 48 km
48 km = 2/3 total d ... total d = 72 km
G = 3 S
G - 5 = 2 (S + 5) ... G = 2 S + 15
Thanks very much, R_scott
1) To calculate the total distance that Joe and Jerry rode together, we need to add up the distances they rode each day.
- On the first day, they rode 1/3 of the total distance.
- On the second day, they rode 1/4 of the remaining distance.
- On the third day, they rode half of the distance left.
- On the last day, they rode the remaining 18 km.
Let's calculate step by step:
- Let's assume the total distance as "D".
- On the first day, Joe and Jerry rode 1/3 * D distance.
- After the first day, the remaining distance is D - (1/3 * D) = 2/3 * D.
- On the second day, they rode 1/4 * (2/3 * D) = 1/6 * D distance.
- After the second day, the remaining distance is 2/3 * D - (1/6 * D) = 1/2 * D.
- On the third day, they rode 1/2 * (1/2 * D) = 1/4 * D distance.
- After the third day, the remaining distance is 1/2 * D - (1/4 * D) = 1/4 * D.
- On the last day, they rode 18 km, which is equal to the remaining distance, 1/4 * D.
So, we have the equation: 1/4 * D = 18.
To find the total distance D, we can multiply both sides of the equation by 4: D = 18 * 4 = 72 km.
Therefore, Joe and Jerry rode a total distance of 72 km together.
2) Let's assume Sam has "S" marbles.
- George has three times as many marbles as Sam, so George has 3 * S marbles.
- If George gives 5 marbles to Sam, he will have 3 * S - 5 marbles left.
- After receiving 5 marbles, Sam will have S + 5 marbles.
- The problem states that after this exchange, George will have twice as many marbles as Sam. So we can write the equation: 3 * S - 5 = 2 * (S + 5).
Let's solve this equation step by step:
- Distribute 2 to the terms inside the parentheses: 3 * S - 5 = 2 * S + 10.
- Combine like terms: 3 * S - 2 * S = 10 + 5.
- Simplify: S = 15.
Therefore, Sam has 15 marbles.
1/) To solve this problem, we need to calculate the distance they rode each day and add them up to find the total distance they rode together. Let's break it down step by step:
First day: Joe and Jerry rode 1/3 of the total distance.
Let's assume the total distance they rode is represented by 'D'. Therefore, on the first day, they rode 1/3 * D.
Second day: They rode 1/4 of the remaining distance.
After the first day, there is 2/3 (1 - 1/3) of the total distance remaining. So, on the second day, they rode 1/4 * (2/3 * D).
Third day: They rode half of the distance left.
After the second day, there is 2/3 * (3/4 * D) = 1/2 * D of the total distance remaining. So, on the third day, they rode 1/2 * (2/3 * (3/4 * D)).
Last day: They rode the remaining 18 km.
Since this is the last day, the distance they rode is equal to the remaining distance, which is 18 km.
Now, let's add up all the distances they rode together:
Total distance = (1/3 * D) + (1/4 * 2/3 * D) + (1/2 * 2/3 * 3/4 * D) + 18 km.
To find the value of D, we can solve the equation:
D = (1/3 * D) + (1/4 * 2/3 * D) + (1/2 * 2/3 * 3/4 * D) + 18 km.
Simplifying the equation, we get:
1 = 1/3 + 1/4 * 2/3 + 1/2 * 2/3 * 3/4 + 18/D.
Now, we can solve this equation to find the value of D, which represents the total distance they rode together.
2/) Let's solve this problem step by step:
Let's assume Sam has 'S' number of marbles.
We are given that George has three times as many marbles as Sam, so George has 3 * S marbles.
If George gives 5 of his marbles to Sam, he will then have twice as many marbles as Sam.
After giving 5 marbles, George will have (3 * S) - 5 marbles.
And Sam will have S + 5 marbles.
According to the given statement, (3 * S) - 5 = 2 * (S + 5).
Let's solve this equation for S.
3S - 5 = 2S + 10
3S - 2S = 10 + 5
S = 15
So, Sam has 15 marbles.