4/9 of a group of students are girls , if there are 17 more boys than girls . how many students are there alltogther
x = 4/9 x + (4/9 x + 17)
x = 153
girls: 68
boys: 85
To find the total number of students in the group, we need to break down the problem step by step.
Let's start by determining the ratio of boys to girls. It is given that 4/9 of the group are girls, which means that 5/9 of the group are boys. We can represent this as:
Girls = 4/9 of the group
Boys = 5/9 of the group
Now, we are also given that there are 17 more boys than girls. This means that the number of boys is 17 greater than the number of girls. We can represent this mathematically as:
Boys = Girls + 17
Since we know the ratio of boys to girls is 5:4, we can create an equation to solve for the number of girls:
Girls = (4/9) * Total
We can substitute this value into the equation for boys:
Boys = (5/9) * Total
Now, let's substitute the value of Boys from our second equation into the first equation:
(5/9) * Total = (4/9) * Total + 17
To solve this equation, we can multiply through by 9:
5 * Total = 4 * Total + 153
Next, we can simplify the equation:
5 * Total - 4 * Total = 153
Total = 153
Therefore, there are a total of 153 students in the group.