Need some help with this question

jameskduong

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Oct 20, 2021
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A gardener has two fertilisers that contain different concentrations of nitrogen. One is 3%
nitrogen and the other is 11% nitrogen. How many pounds of each should she mix to obtain
20 pounds of a 9% concentration?
1. Define the variables if they are not already defined in the problem, i.e. Let x be ................
and y be ................ (10 marks).
2. How many equations do we need to model the problem? Write down the equations in
terms of the variables (20 marks).
 
Last edited:
Hi James. Symbols x and y are variables. They represent unknown quantities. The exercise statement asks, "how much of each". What two specific quantities are they asking about? Those two amounts are what x and y represent -- the unknowns they want you to find.

?
 
You wan to answer the question "How many pounds of each kind of fertilizer" so you can sayy "x is the number of pounds of the first fertilizer" and "y is the number of pounds of the second kind of fertilizer,"

Since you want to determine two values, you will need two equations.

x is the number of pounds of the first kind of fertilizer and y is the number of pounds of the second kind of fertilier. So x+ y= what?

We are told that the first kind of fertilizer contains 3% nitrogen. Do you understand that x pounds of this fertilizer will contain ,03x pounds of fertilizer?

We are told that the second kind of fertilizer contains 11% nitrogen. Do you understand that y pounds of this fertilizer will contain .11y pounds of nitrogen?

You want to add those two together getting 20 pounds of a 9% fertilier which will contain ,09(20)= 1.8 pounds of nitrogen.

So the .03x and .11y pounds of nitrogen must total 1,8 pounds of nitrogen. So what is the second equation?

Now solve those two equations for x and y.
 
Hi James. Symbols x and y are variables. They represent unknown quantities. The exercise statement asks, "how much of each". What two specific quantities are they asking about? Those two amounts are what x and y represent -- the unknowns they want you to find.

?
okay noted
You wan to answer the question "How many pounds of each kind of fertilizer" so you can sayy "x is the number of pounds of the first fertilizer" and "y is the number of pounds of the second kind of fertilizer,"

Since you want to determine two values, you will need two equations.

x is the number of pounds of the first kind of fertilizer and y is the number of pounds of the second kind of fertilier. So x+ y= what?

We are told that the first kind of fertilizer contains 3% nitrogen. Do you understand that x pounds of this fertilizer will contain ,03x pounds of fertilizer?

We are told that the second kind of fertilizer contains 11% nitrogen. Do you understand that y pounds of this fertilizer will contain .11y pounds of nitrogen?

You want to add those two together getting 20 pounds of a 9% fertilier which will contain ,09(20)= 1.8 pounds of nitrogen.

So the .03x and .11y pounds of nitrogen must total 1,8 pounds of nitrogen. So what is the second equation?

Now solve those two equations for x and y.
thanks for the help
 
so what is it meant to be?
because I don't quite understand how to get the two equations
let x = number of pounds of 3% nitrogen
y = number of pounds of 11% nitrogen

x + y = 20

x(0.03) + y(0.11) = 20(0.09) or, after multiplying each term by 100 to clear the decimals …
3x + 11y = 180

solve the system for x and y
 
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