1. Pete and Marie had 360 marbles. Pete had 40 fewer marbles than Marie. Pete gave his brother 3/8 of his marbles. How many marbles did Pete have left?
2. Four children shared some sweets among themselves. Adam took 1/8 of the total number of sweets while Barry took 1/4 of them. Kaden took 1/4 of the remaining sweets and Shaun took the rest. If Barry took 20 more sweets than Adam, how many sweets did Shaun take?
Can you check my answers?
1. 100
360 - 40 = 320
Pete’s marbles -> 320 / 2 = 160
Number of marbles Pete gave his brother -> 3/8 * 160 = 60
Number of marbles Pete had left -> 160 - 60 = 100
Pete had 100 marbles left.
2. 75
1/4 = 2/8
2/8 - 1/8 = 1/8
1/8 of total = 20
Adam took 20 sweets.
Barry -> 20 + 20 = 40
Total sweets -> 8 * 20 = 160
Remaining sweets -> 160 - 40 - 20 = 100
Kaden -> 1/4 * 100 = 25
Shaun 100 - 25 = 75
Shaun took 75 sweets.
1. Well, it seems like Pete really had to give Marie a "marbleous" surprise by having fewer marbles. So, if Pete had 40 fewer marbles than Marie, that means Marie had 200 marbles. Now, Pete gave his brother 3/8 of his marbles, which is like sharing the "marbleicious" love. Let's do some math magic - Pete had 360/8 = 45 marbles. And his brother got 3/8 * 45 = 13.5 marbles. But hey, we can't have half a marble, right? So, Pete had 45 - 13.5 = 31.5 marbles left, or in simpler terms, 31.5 marbles or 31 marbles and a "half-marble".
2. It looks like these kids have quite a sweet tooth! So, let's see. If Adam took 1/8 of the sweets and Barry took 1/4, it means they had 8 and 4 parts, respectively, out of a total of 8+4 = 12 parts of sweets. Now, we know that Barry took 20 more sweets than Adam, which can give us a sugar rush of information. If 4 parts equal 20 sweets, then 1 part is equal to 20/4 = 5 sweets. So, Adam had 5 sweets and Barry had 20 + 5 = 25 sweets. Now, Kaden takes 1/4 of the remaining sweets, which is 3 parts out of 12 parts. That leaves us with 12-3 = 9 parts. And since Shaun took the rest, he must have taken the remaining 9 parts, which is equal to 9 * 5 = 45 sweets. So, Shaun merrily devoured 45 sugar-coated delights!
To answer these questions, let's break down the information step by step.
1. Pete and Marie had 360 marbles. Pete had 40 fewer marbles than Marie.
Let's assume that Marie had x marbles.
Pete had 40 fewer marbles than Marie, so Pete had x - 40 marbles.
The total number of marbles they had is 360, so we can set up an equation:
x + (x - 40) = 360
Simplifying the equation, we get:
2x - 40 = 360
2x = 400
x = 200
Marie had 200 marbles, and Pete had 40 fewer marbles, which means Pete had:
200 - 40 = 160 marbles.
2. Four children shared some sweets among themselves. Adam took 1/8 of the total number of sweets, while Barry took 1/4 of them. Kaden took 1/4 of the remaining sweets, and Shaun took the rest.
Let's assume the total number of sweets is x.
Adam took 1/8 of the total, so Adam took (1/8) * x sweets.
Barry took 1/4 of the total, so Barry took (1/4) * x sweets.
The remaining sweets are: x - (1/8) * x - (1/4) * x
Simplifying, we get: 7/8x - 1/4x = (7/8 - 1/4) * x = (7/8 - 2/8) * x = (5/8) * x = 5x / 8
Kaden took 1/4 of the remaining sweets, so Kaden took (1/4) * (5x / 8) = 5x / 32
Barry took 20 more sweets than Adam, so we can set up an equation:
(1/4) * x = (1/8) * x + 20
Simplifying the equation, we get:
(1/4 - 1/8) * x = 20
(2/8 - 1/8) * x = 20
(1/8) * x = 20
x/8 = 20
x = 20 * 8
x = 160
Now that we know the total number of sweets is 160, we can find out how many sweets Shaun took.
Shaun took the remaining sweets, which is 5x / 8.
So Shaun took (5/8) * 160 = 5 * 20 = 100 sweets.
Therefore, Shaun took 100 sweets.
1. To solve this problem, let's break it down step by step.
First, let's represent the number of marbles Pete had as "P" and the number of marbles Marie had as "M". We are given that Pete had 40 fewer marbles than Marie, which in equation form is P = M - 40.
Next, we know that Pete and Marie had a total of 360 marbles, so we can write the equation P + M = 360.
Substituting the value of P from the first equation into the second equation, we get (M - 40) + M = 360. Simplifying this equation, we have 2M - 40 = 360.
Adding 40 to both sides of the equation, we get 2M = 400.
Dividing both sides of the equation by 2, we find that M = 200.
Now that we know the value of M, we can substitute it back into the equation P = M - 40 to find the value of P. P = 200 - 40 = 160.
So, Pete had 160 marbles.
Lastly, we are told that Pete gave his brother 3/8 of his marbles. To find out how many marbles Pete gave away, we multiply 160 by 3/8: (160 * 3) / 8 = 480 / 8 = 60.
Therefore, Pete gave away 60 marbles. To find out how many marbles Pete had left, we subtract 60 from 160: 160 - 60 = 100.
Thus, Pete had 100 marbles left.
2. Let's solve this problem step by step as well.
First, let's represent the total number of sweets as "T". We know that Adam took 1/8 of the sweets, so we can write this as (1/8)T. Barry took 1/4 of the sweets, which can be written as (1/4)T.
We are also given that Barry took 20 more sweets than Adam, so we can create the equation (1/4)T = (1/8)T + 20.
To simplify this equation, we need to find a common denominator for 1/4 and 1/8, which is 8. So, we can rewrite the equation as (2/8)T = (1/8)T + 20.
Combining the fractions on the left side of the equation, we have (2/8)T = (1/8)T + 20.
Simplifying further, we get (2/8)T - (1/8)T = 20.
This simplifies to (1/8)T = 20.
Multiplying both sides of the equation by 8, we find T = 160.
Therefore, the total number of sweets is 160.
Next, we know that Kaden took 1/4 of the remaining sweets, which is (1/4)(160) = 40.
To find out how many sweets Shaun took, we need to subtract the sweets taken by Adam, Barry, and Kaden from the total.
Adam took (1/8)(160) = 20 sweets.
Barry took (1/4)(160) = 40 sweets.
Kaden took 40 sweets.
So, the remaining sweets are 160 - 20 - 40 - 40 = 60.
Hence, Shaun took 60 sweets.