Dear Everyone,
Disclaimer: This question is not a homework question. I am using a outdate book (meaning that the book, College Algebra by Richard Heineman, is not taught out of) to use this technique (as you will read below).
I was given a document about problem solving technique by my previous tutoring supervisor and Intermediate Algebra instructor at my undergraduate university. The technique by using some transitional words (let, then, but, so, therefore) in the solution in order for the students not to be overwhelm and confused on the story problems. For instead,
"Suppose in designing a house, the living room is to be thrice as long as it is wide. The total area of the room is 507 square feet. What should be the length of the room?"
Solution to this example:
Let [MATH]w[/MATH] be the width. Then the length is [MATH] 3w[/MATH], and the area will be [MATH] (3w)(w)=3w^2[/MATH]. But we know the total area is 507. So [MATH]3w^2=507[/MATH]. After we divide 3 and take the positive root on both side of the equation, we discovered [MATH]w=13[/MATH]. Therefore (or any synonym), the length of the room is 39 feet because [MATH] 3 \cdot 13=39[/MATH].
Here is my problem, Exercise 15 problem 5: A vending machine contains $4.30 consisting of nickels and dimes. How many of each if the total number of coins is 60?
I have notes some facts in the problem: There is 4.30 dollars. We know that 2 nickels is equivalent to one dime. We have something with 60 coins.
But I am struck on how to set it up.
Here is what I think the solution should look like:
Let [MATH]n[/MATH] be the number of nickels in the vending machine. Then the machine have a total of $4.30. But the machine has 60 coins all together. So....
Disclaimer: This question is not a homework question. I am using a outdate book (meaning that the book, College Algebra by Richard Heineman, is not taught out of) to use this technique (as you will read below).
I was given a document about problem solving technique by my previous tutoring supervisor and Intermediate Algebra instructor at my undergraduate university. The technique by using some transitional words (let, then, but, so, therefore) in the solution in order for the students not to be overwhelm and confused on the story problems. For instead,
"Suppose in designing a house, the living room is to be thrice as long as it is wide. The total area of the room is 507 square feet. What should be the length of the room?"
Solution to this example:
Let [MATH]w[/MATH] be the width. Then the length is [MATH] 3w[/MATH], and the area will be [MATH] (3w)(w)=3w^2[/MATH]. But we know the total area is 507. So [MATH]3w^2=507[/MATH]. After we divide 3 and take the positive root on both side of the equation, we discovered [MATH]w=13[/MATH]. Therefore (or any synonym), the length of the room is 39 feet because [MATH] 3 \cdot 13=39[/MATH].
Here is my problem, Exercise 15 problem 5: A vending machine contains $4.30 consisting of nickels and dimes. How many of each if the total number of coins is 60?
I have notes some facts in the problem: There is 4.30 dollars. We know that 2 nickels is equivalent to one dime. We have something with 60 coins.
But I am struck on how to set it up.
Here is what I think the solution should look like:
Let [MATH]n[/MATH] be the number of nickels in the vending machine. Then the machine have a total of $4.30. But the machine has 60 coins all together. So....
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