Determining the Number of Adult Tickets from a Ratio of 4 is to 5

Question

The ratio of adult tickets to student tickets for the play was 4:5. If the sum of the adult tickets and one half of the student tickets is 260, how many adult tickets were sold?

The choices are as follow:

80

100

160

200

None of the above

I tried to solve this and here's my equation:

4x + 5[(260-x)/2] = 260

But this does not yield the answer as stated in my answer key which is 160.

Please help me translate this problem into an equation correctly.

PS I am a college student struggling with word problems, and this ratio problem gives me headache.

Answer 1

Your equation seems not right.If $4x$is the sum of adult tickets then the sum of student tickets should be $5x$,which means the equation should be$$ 4x+\frac{5x}{2}=260$$ And $x=40$.

Answer 2

System of Equations:

$A/S = 4/5$

$A+(S/2)=260$

Where A is the number of adult tickets and S is the number of student tickets. Can you solve that?

Edit: You asked to translate the problem into an equation, so might as well go up to that step.

$S/A = 5/4$

$A + (5A/8) = 260$

Now simply solve for A.