Vinegar problems

Question

A chef plans to mix 100% vinegar with Italian dressing the talion dressing contains 4% vinegar the chef wants to make 320 mL of a make sure that contains 13% vinegar how much vinegar and how much Italian dressing should she use

Answer 1

x is the vinegar and y is the salad dressing

x + y = 320 <--- total mixture must be 320

AND

x + 0.04y = 0.13*320 <--- amount of vinegar in the mixture

x + 0.04y = 41.6

100x + 4y = 4160

100x + 4(320 -x) = 4160

100x + 1280 - 4x = 4160

96x + 1280 = 4160

96x = 2880

x = 30

30 mL of vinegar and 290 mL of the salad dressing

contains 30 + .0.04*290 = 30 +11.6 = 41.6 mL of vinegar.

which is 41.6/320 = 0.13 = 13%

the answer in bold is correct