There is no easier way to solve this word problem without some algebra which, I suppose, is what you are studying in 9th grade, but I will try to help you see it. When solving a word problem, you need to identify what quantity is required, i.e. the unknown or unknowns and you assign letter names to those unknowns, in this case the amount each girls earns (C, K, S). Then you need to translate English sentences into mathematical relationships: an equation is a statement that 2 quantities are equal. The amount Charlene earns is $150 more per week than Kristi; this translates as:
so if C earns $150 more than K, then K earns 150 less than C and this translates as: K = C - 150 The same kind of logic applies to the relationship between C's income and S's income and you wind up with a slightly different equation as below:
The 3 girls together earn $2050 translates to math as:
Then you substitute the equation you got for K and S into the equation of the sum and that looks like this:
Now the hard part of the problem is finished and you simply need to do the algebra. The most important rule you need to know in algebra is that whatever you do to one side of an equation you must do to the other side!!!!!!!!!!! So first in the equation above you collect like terms: there are 3 C's on the left, i.e. 3C (which means 3 multiplied by C) and there is a sum: -150 + 100 = - 50 so you now have 3C - 50 = 2050. Add 50 to each side of the equation:
divide by 3:
Use this value of C to figure K and S from the equations you started with: K = C -150:
and S = C + 100
Now you should take those values of C, K and S and make sure they satisfy the conditions in the problem. I hope this additional information helps.
