There were 5 times as many strawberries as blueberries in a container. Joel ate half of the number of strawberries and 120 strawberries were left in the container. How many strawberries and blueberries were in the container at first?
Well, well, well, looks like Joel couldn't resist those juicy strawberries! Alright, let's get cracking on this fruity puzzle.
Let's assume that the initial number of blueberries in the container was "x." Since there were five times as many strawberries as blueberries, we can say that the initial number of strawberries was 5x.
Now, Joel decides to munch on half of the strawberries, which means he consumed 5x/2 strawberries. After this tasty strawberry feast, we are left with 120 strawberries in the container.
So, the equation we can form is: 5x/2 = 120.
Solving this equation, we find that x (the initial number of blueberries) is equal to 48.
Therefore, the initial number of strawberries was 5x, which gives us 5 * 48 = 240 strawberries.
In total, at first, there were 240 strawberries and 48 blueberries in the container. Joel sure had his fill!
Let's break down the problem step by step.
Step 1: Let's assign variables to the unknown quantities.
Let:
x be the number of blueberries in the container.
5x be the number of strawberries in the container.
Step 2: Calculate the new number of strawberries after Joel ate half of them.
Since Joel ate half of the number of strawberries, there were 5x/2 strawberries left in the container.
Step 3: Determine the total number of strawberries and blueberries in the container after Joel ate half of the strawberries.
The total number of strawberries and blueberries left in the container is given as 120. So, we can write the equation:
5x/2 + x = 120
Step 4: Solve the equation for x, which represents the number of blueberries.
To simplify the equation, let's get rid of the fraction by multiplying both sides of the equation by 2:
2 * (5x/2) + 2 * x = 2 * 120
5x + 2x = 240
7x = 240
Divide both sides of the equation by 7 to solve for x:
x = 240/7
x ≈ 34.29
Since we can't have a fraction of a berry, we'll assume that there were 34 blueberries in the container.
Step 5: Calculate the number of strawberries in the container.
We know that there were 5 times as many strawberries as blueberries, so:
5x = 5 * 34 ≈ 170
Therefore, there were approximately 170 strawberries and 34 blueberries in the container at first.
To determine the original number of strawberries and blueberries in the container, we can follow these steps:
Step 1: Let's assume the initial number of blueberries in the container is 'x'.
Step 2: Since there were 5 times as many strawberries as blueberries, the initial number of strawberries in the container would be 5x.
Step 3: Joel ate half of the number of strawberries, which means 5x/2 strawberries were consumed. Therefore, only 5x/2 strawberries were left in the container.
Step 4: Given that there were 120 strawberries left, we can set up the equation: 5x/2 = 120.
Step 5: To solve for x, we need to isolate it on one side of the equation. Multiply both sides of the equation by 2/5: (2/5)*5x/2 = (2/5)*120.
Step 6: Simplifying the equation gives us: x = 48.
Step 7: Substitute the value of x back into the equation 5x to find the number of strawberries: 5 * 48 = 240.
Step 8: Thus, at first, there were 240 strawberries and 48 blueberries in the container.
s = 5b
s/2 = 120
Now finish it off