Math word help

Question

a chef plans to mix 100% vinegar with italian dressing. The Italian dressing contains 13% . The chef wants to make 150 millimeters of mixture that contains 42% vinegar. How much vinegar and how much Italian dressing should she use?

Answer 1

(x mls)(100%) + (150 mls - x mls)(13%) = (150 mls)(42%)

100 x + 1950 - 13 x = 6300

87x = 4350

x = 50 mls of 100%

150 - 50 = 100 mls of 13%

 

Done by alligation:

Have.......Want.......Need......

100%.......................29........

................42%.....................

13%.........................58.......

Total parts...............87.......

 

87parts = 150mls, 

 

1 part = 1.724 mls

1.72 x 29 = 50 mls of 100%

1.72 x 58 = 100 mls of 13%

 

Answer 2

Hi, Tracie.

 

Okay, let X = amount of vinegar needed

 

150 - X = amount of dressing needed in (milliliters, not millimeters (that is linear measurement)

 

X + .13(150 - X) = .42(150)

X + 19.5 - .13X = 63

.87X = 43.5

X = 50 mL

 

150 - X = 100 mL

 

So, she needs 50 mL of vinegar and 100 mL of Italian dressing