<em>x > 6</em>
- <em>Step-by-step explanation:</em>
<em>Hi there ! </em>
<em>1/2 x + ²⁾3 < ²⁾2x - ²⁾6</em>
<em>x + 6 < 4x - 12</em>
<em>6 + 12 < 4x - x</em>
<em>18 < 3x</em>
<em>3x > 18</em>
<em>x > 18/3</em>
<em>x > 6</em>
<em>Good luck ! </em>
8x^2-50 is your answer hopes this helps
0.067 is the answer for this
Answer:
Step-by-step explanation:
Let x represent the number of batches of soap that Lilth makes.
Let y represent the number of batches of lotion that Lilth makes.
It takes her 20 minutes(20/60 = 1/3 hours) to make a batch of soap and 35 minutes(35/60 = 7/12 hours) to make a batch of lotion. Lilth has 20 hours available to make soap and lotion. This means that
x/3 + 7y/12 = 20
4x + 7y = 240- - - - - - - - - - -1
The cost of producing each batch are $5 for the soap and $15 for the lotion. The materials to make the soap and lotion must cost at most $325. This means that
5x + 15y ≤ 325 - - - - - - - - -2
4x = 240 - 7y
x = (240 - 7y)/4
Substituting
5(240 - 7y)/4 + 15y ≤ 325
(1200 - 35y)/4 + 15y ≤ 325
1200 - 35y + 60y ≤ 1300
25y ≤ 1300 - 1200
25y ≤ 100
y ≤ 100/25
y ≤ 4
4x + 7 × 4 = 240
4x + 28 = 240
4x = 212
x = 212/4 = 53
Therefore, the solution (53, 4) means that she would make at most 53 batches of soap and at most 4 batches of lotion
The price was reduced by 34%, so she paid 100-34 = 66% of the original price.
16,000 x 0.66 = 10,560
She paid $10,560
