We can solve this question easiest by putting it as 2 equations.

First, well put the original equation, 2c+5b=55,000. B stands for the cost of backyard pool weddings and c stands for the cost of carribean weddings.

We got this equation because the question states that there were 2 carribean weddings and 5 pool weddings, and the amount of money obtained was $55,000 total as a result.

Now, we’ll put the extra information into an equation, c-10,000=b. We got this equation because it clearly states that backyard pool weddings cost 10,000 less than Caribbean, so c-10,000=b.
Now, we have to solve. Since the first equation has 2 variables, it is unsolvable. This is where the second equation comes in. We can rewrite c-10,000=b as b+10,000=c.

Now, since b+10,000=c, substitute b+10,000 for c in the first equation.
The result is 2(b+10,000)+5b=55,000.
Now that we only have one variable in the equation, it is solvable.
20,000+7b=55,000
7b=55,000
B=7,857
Now to solve for c, insert 7,857 for b in the second equation.
7,857+10,000=c
17,857=c
The cost of carribean weddings was $17,857.
The cost of a backyard pool wedding was $7,857.
Hope this helps!

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4 years ago