Answer:
<u>The equations system is:</u>
<u>x + y = 10</u>
<u>0.5x + 0.9y = 6</u>
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Liters of 60% acid solution needed = 10
x = Number of liters of the 50% solution
y = Number of liters of the 90% solution
2. Which equation represents the total liters of acid that are needed?
There are two equations needed:
The first one related to the total liters needed, 10 in this case:
x + y = 10
The second one related to the acid concentration of the 10 liters:
0.5x + 0.9y = 10 * 0.6
0.5x + 0.9y = 6
<u>The equations system is:</u>
<u>x + y = 10</u>
<u>0.5x + 0.9y = 6</u>
Solving for x and y in the 2nd equation, we have:
0.5 (10 - y) + 0.9y = 6
5 - 0.5y + 0.9y = 6
0.4y = 6 - 5
0.4y = 1
y = 1/0.4 = 2.5 ⇒ x = 7.5 (10 - 2.5)
The scientist can mix 7.5 liters of the 50% acid solution and 2.5 liters of the 90% acid solution to get the 10 liters of the 60% acid solution.
Answer:
13, they could all split up into groups of 1
Step-by-step explanation:
Answer:tickets in Germany cost $8.93
tickets in France cost $8.85
Step-by-step explanation:
Let x represent the cost of a movie ticket in Germany.
Let y represent the cost of a movie ticket in France.
Four movie tickets in Germany plus 3 movie tickets in France cost &62.27. This means that
4x + 3y = 62.27 - - - - - - - - 1
three tickets in Germany plus 4 tickets in France cost $62.19
This means that
3x + 4y = 62.19 - - - - - - - - -2
Multiplying equation 1 by 3 and equation 2 by 4. It becomes
12x + 9y = 186.81
12x + 16y = 248.76
Subtracting,
- 7y = - 61.95
y = - 61.95/7
y = 8.85
Substituting y = 8.85 into equation 1, it becomes
4x + 3×8.85 = 62.27
4x + 26.55 = 62.27
4x = 62.27 - 26.55
4x = 35.72
x = 35.72/4 = 8.93