Line 1 because the question says “less than 4”
<span>let x = the number of liters of the 20% solution.
let y = the number of liters of the 60% solution.
you want x + y to be equal to 40 liters.
x is the number of liters total in the first solution.
y is the number of liters total in the second solution.
you want .2 * x + .6 * y to be equal to .35 * 40
.2 * x is the number of liters of acid in the first solution.
.6 * y is the number of liters of acid in the second solution.
.35 * 40 is the number of liters of acid in the final solution.
you have two equations that need to be solved simultaneously.
they are:
x + y = 40
.2x + .6y = .35*40
simplify these equations to get:
x + y = 40
.2x + .6y = 14
you can solve by substitution or by elimination or by graphing.
i will solve this one by graphing.
this means to graph both equations and find the intersection.
the graph looks like this:
the graph says the intersection is at the coordinate point of (25,15).
this means that x = 25 and y = 15.
x is the number of liters of the 20% solution.
y is the number of liters of the 60% solution.
the formula of .2x + .6y = 14 becomes .2 * 25 + .6 * 15 = 14.
simplify this equation to get 14 = 14.
this confirms the solution is good.
</span>
Remark
This is a nice problem especially if you like blue jays! They actually do things like this.
Equations.
Let the number of trees = T
Let the number of acorns = A
20*T = A + 4 Read that carefully. There are 4 acorns left over. The number stored = A. The left over ones make 4 more than were stored.
Second equation
18*T = A - 4 Here we have 4 less than could be stored to full capacity.
Solution
20T = A + 4
<u>18T = A - 4 </u> Subtract
2T = 8 Divide by 2
T = 8/2; T = 4 Answer
20T = A + 4
20*4 = A
80 - 4 = A
A = 76 Answer
Answers
The number of Trees = T
The number of acorns = 76
Answer: Inductive Reasoning
Step-by-step explanation: The process of arriving at a general conclusion based on observations of specific examples. When you try to find the pattern for a list of numbers or visuals, you are using inductive reasoning.
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