At a banquet the ratio if the number of boys to the number of girls is 5:3. Halfway tjrough the banquet 20 boys leave and the ratio bexomes 5:4. How many girls are at thebbanquet?
let the number of boys be 5x
let the number of girls be 3x
during banket, 20 boys leave
(5x-20)/3x = 5/4
20x - 80 = 15x
5x = 80
x = 16
number of girls is 3x or 48.
check:
original:
boys = 80
girls = 48
after leaving:
boys = 60
girls = 48
ratio is 60:48 = 5 : 4
reiny can you explain the equation more? is the / a division symbol? i still don't understand how you got 16.
48
ratios are fractions so yes the "/" is a division sign. the 2 ratios become 5/3=5/4, but you have to incorporate the minus 20. So 5x-20 represent to boys, and 3x is the girls then to make it equate the 5:4 ratio you place it in an algebraic equation and cross multiply. (5x-20) X 4= 3x X 5 = 20x-80= 15x
20x-15x= 80 = 5x=80 or x =80/5 which equals 16,so x =16.
Where you get the 80 from...?
Well, well, well, looks like we're having a math problem at the banquet. Let's see if I can help you with that.
First, let's assume that we have 5x boys and 3x girls at the start of the banquet, where x is just a fancy placeholder for the number of something.
Now, halfway through the banquet, 20 boys leave, which means we're left with 5x - 20 boys. And the ratio of boys to girls becomes 5:4. So, we can set up an equation:
(5x - 20) / (3x) = 5/4
Alright, let's do some math magic:
4(5x - 20) = 5(3x)
20x - 80 = 15x
5x = 80
x = 16
Now that we know x, let's find the number of girls:
3x = 3(16) = 48
Voila! There are 48 girls at the banquet. Hope this answer didn't make a clown of itself!
To find the number of girls at the banquet, we can follow these steps:
Step 1: Set up the ratio equation based on the given information.
Let's assume the initial number of boys is 5x and the initial number of girls is 3x, where x is a constant.
According to the given ratio, we have:
Number of boys: Number of girls = 5x : 3x
Step 2: Calculate the new number of boys and girls after 20 boys leave.
Since halfway through the banquet 20 boys leave, the new number of boys becomes (5x - 20), and the ratio changes to 5:4.
Therefore, we have:
Number of boys: Number of girls = (5x - 20) : 4
Step 3: Set up an equation using the ratio equations from Step 1 and Step 2.
We can set up the equation based on the ratio of boys and girls before and after 20 boys leave:
5x : 3x = (5x - 20) : 4
Step 4: Solve the equation to find the value of x.
To solve the equation, we can cross-multiply:
5x * 4 = 3x * (5x - 20)
20x = 15x^2 - 60x
Step 5: Simplify and rearrange the equation.
Rearranging the equation in quadratic form:
15x^2 - 60x - 20x = 0
15x^2 - 80x = 0
Dividing both sides by 5x:
15x - 80 = 0
15x = 80
x = 80 / 15
x ≈ 5.33
Step 6: Calculate the number of girls.
Substitute the value of x back into the initial ratio equation to find the number of girls:
Number of girls = 3x ≈ 3 * 5.33 ≈ 15.99
Since we cannot have a fraction of a person, we can round up the number of girls to the nearest whole number.
Therefore, there are approximately 16 girls at the banquet.