Find x and y in x+y=3421 and 23% of x + 13.5% of y = 684.34

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In summary, to find the values of x and y so that both equations give correct answers, we can use substitution to solve for x and then find y using the second equation. The values for x and y are approximately 1816 and 1605, respectively.
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northuk
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I need help with the following problem. I will appreciate any help to solve this:

x+y=3421
23% of x + 13.5% of y = 684.34

What are the values of x and y so the both of above equations give correct answers.
 
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northuk said:
I need help with the following problem. I will appreciate any help to solve this:

x+y=3421
23% of x + 13.5% of y = 684.34

What are the values of x and y so the both of above equations give correct answers.
"23% of x + 13.5% of y = 684.34" is equivalent to the equation
0.23x+ 0.135y= 684.34.

x+ y= 3421 is the same as y= 3421- x so the second equation can be written
0.23x+ 0.135(3421- x)= 684.34.

0.135*3421= 461.835 so that equation is the same as 0.23x+ 461.835- 0.135x= 684.34.

We can write that as (0.23- 0.135)x= 684.34- 461.835 and, doing the arithmetic,
0.095x= 172.505 so x= 172.505/0.095= 1816, approximately. Then y= 3421- x= 3421- 1816= 1605. Again, approximately. I have rounded to the nearest integer. Since one the given data had only 2 significant figures that should be accurate enough.
 

FAQ: Find x and y in x+y=3421 and 23% of x + 13.5% of y = 684.34

How do I solve for x and y in the given equations?

In order to solve for x and y in the given equations, you can use the method of substitution. First, rearrange the equations to solve for one variable in terms of the other. Then, substitute the value of that variable into the other equation and solve for the remaining variable. Finally, plug in the value of the first variable into the original equation to find the value of the other variable.

Can I use a calculator to solve these equations?

Yes, you can use a calculator to solve these equations. However, it is recommended to show your work and steps in order to receive full credit for your solution.

How do I handle the percentages in the equations?

In order to handle the percentages, you can convert them to decimal form by dividing the percentage by 100. For example, 23% would be converted to 0.23. Then, you can use this decimal in the equations just like any other number.

Can I check my solution to make sure it is correct?

Yes, you can always check your solution by plugging in the values of x and y into the original equations and seeing if they satisfy the equations. If the values make the equations true, then your solution is correct.

Are there any special rules or formulas I need to know to solve these equations?

No, there are no special rules or formulas required to solve these equations. However, it is important to have a strong understanding of basic algebra concepts such as solving equations and manipulating variables.

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