April G. answered • 09/05/12

Math tutor

The wording on the question is a little confusing, but I think I get what you're saying. Someone has thrown 50 darts at a dart board where a bullseye is worth 7 points and anything else is worth 2 points. The person has 152 points, and the question is to find out how many bullseyes were made.

I think the numbers here are a bit off, which might be why you're having trouble. I'll walk through how I would solve the problem using equations and explain.

There are 2 types of results from throwing a dart, bullseye or not. We don't know how many of either, so we'll let *b*=number of bullseyes and *n* = number of non-bullseyes.

Since there are 50 darts, we know that: **b + n = 50**

The total number of points is 152: bullseye points + non-bullseye points. All the bullseye points would be 7*b (7b) and non-bullseye points would be 2*n (2n). So we could also write **7b + 2n = 152**

Now we have the system of equations

b + n = 50

7b + 2n = 152

I'm going to use substitution to solve this problem. Look at the first equation: if we subtract b from both sides, we see that n = 50-b. Substitute (50-b) in place of n in the 2nd equation.

**7b + 2(50-b) = 152****7b + 100 - 2b = 152*** (distribute)***5b +100 = 152** *(combine like terms)***5b = 52** *(subtract 100 from both sides)***b = 10.4** *(divide both sides by 5)*

Does this answer make sense? Can you have 10.4 bullseyes? Nope! Now, if there were 51 darts thrown instead, everything works out rather nicely.