A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 5% vinegar, and the second brand contains 15% vinegar. The chef wants to make 240 milliliters of a dressing that is 8% vinegar. How much of each brand should she use?

168 ml of 5%,

72 ml of 15%

Step-by-step explanation:

X + Y = 240

X = 240 - Y

0.05X + 0.15Y = 0.08 (240)

0.05X + 0.15Y = 19.2

X + 3Y = 384

240 - Y + 3Y = 384

2Y = 144

Y = 72

X = 240 - 72

X = 168

You want to setup an equation that will match the word problem. Let's call the amount of the first brand, F and the amount of the second brand, S.

We want the total mixture to be 310mL so: F + S = 310

Also, you want the total mixture to contain 8% vinegar so:.06F +.11S =.08 (310)

Now, we can solve the system of equations using substitution.

F + S = 310

.06F +.11S =.08 (310)

F = 310 - S [solve 1st equation for F]

.06 (310 - S) +.11S =.08 (310) [substitute into 2nd equation]

18.6 -.06S +.11S = 24.8

.05S = 6.2

S = 124

F + 124 = 310 [substitute answer for S back into original equation]

F = 186

Answer: to make a 310mL mixture that contains 8% vinegar, use 186mL of the first brand and 124mL of the second brand.