SOLUTION: How do I solve. Jayce bought 2 bath towels and 3 hand towels for $35. His sister jayna bought 3 bath towels and 3 hand towels for $45. Determine the prices of a bath towel and hand

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Question 1141822: How do I solve. Jayce bought 2 bath towels and 3 hand towels for $35. His sister jayna bought 3 bath towels and 3 hand towels for $45. Determine the prices of a bath towel and hand towel.
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
b = price of a bath towel.
h = price of a hand towel.

2b + 3h = 35
3b + 3h = 45

first equation is for jayce.
second equation is for jayna.

subtract the first equation from the second to get:

b = 10

in the first original equation, replace b with 10 to get 2 * 10 + 3h = 35

simplify to get 20 + 3h = 35

subtract 20 from both sides to get 3h = 15

solve for h to get h = 5

you have b = 10 and h = 5

replace b and h in the two original equations to get:

2b + 3h = 35 becomes 2*10 + 3*5 = 35 which becomes 35 = 35
3b + 3h = 45 becomes 3*10 + 3*5 = 45 which becomes 45 = 45

both original equations are true when you replace b with 10 and h with 5.

your solution is that the price of a bath towel is 10 and the price of a hand towel is 5.





Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

            Actually, this problem is for MENTAL solution, and I will show you right now how to solve it mentally, easy and elegantly. 


If you read the problem attentively, you will notice, that the difference in items bought by two women, is exactly 1 bath towel.


The difference in the payed cost is $45 - $35 = 10 dollars.


Hence, one bath towel price is 10 dollars.   (Half of the problem is just solved (!) ).


Next, Jayce paid 2*10 = 20 dollars for 2 bath towel -- hence, the cost of 3 hand towels is 35 - 20 = 15 dollars.


From it, you get the price of one hand towel  15/3 = 5 dollars.


            The problem is just solved !


---------------------

Many problems, that from the first glance seems to be problems for systems of two equations in two unknowns,
actually, can be solved MENTALLY, as this one.

To see other problems solved by similar way, look into the lesson
    - Solving mentally word problems on two equations in two unknowns
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic "Systems of two linear equations in two unknowns".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.



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