SOLUTION: I am having trouble understanding how to do this type of problem... I know the answer of the second by plugging in (guessing) But I need to know how to do the formula and steps fo

Question 110101This question is from textbook Algebra Structure and method book 1
: I am having trouble understanding how to do this type of problem... I know the answer of the second by plugging in (guessing) But I need to know how to do the formula and steps for a test on Friday.
1. Jessica has 16 dimes and quarters. Whitney has twice as many dimes and 1/3 as many quarters as Jessica has. If they both have the same amount of money, what coins does each have?
2.Esteban has 16 coins that total $3.00 If he has only nickels and quarters, how many quarters does he have?
Thank you for your help! This question is from textbook Algebra Structure and method book 1

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1. Jessica has 16 dimes and quarters. Whitney has twice as many dimes and 1/3 as many quarters as Jessica has. If they both have the same amount of money, what coins does each have?
---------------
Using two variables:
Let x be the # of dimes ; let y be the # of quarters.
EQUATIONS:
Jessica DATA:
x + y = 16
Value of her coins 10x+25y cents
--------------
Whitney DATA:
has 2x dimes and (y/3) quarters
Value of her coins: 20x + (25/3)y cents
----------------
EQUATIONS:
x + y = 16
x = 16-y
--------
10x+25y = 20x + (25/3)y
10x = (50/3)y
x = (5/3)y
------------------
Substitute to solve for "y":
16-y = (5/3)y
16 = 8/3 y
2 = (1/3)y
y = 6 (# quarters Jessica has)
x=16-y=10 (# of dimes Jessica has)
Note: This adds to $2.50
------------
2x = 20 (# of dimes Whitney has)
(1/3)y = 2 (# of quarters Whitney has)
Note: This also adds to $2.50
==========================================

2.Esteban has 16 coins that total $3.00 If he has only nickels and quarters, how many quarters does he have?
---------------------------
Using only one variable:
Let number of nickels be "x" ; value of these is 5x cents
# of quarters is "16-x" ; value of these is 25(16-x)= 400-25x cents
-------------------------
EQUATION:
value + value = 300 cents
5x + 400-25x = 300
-20x = -100
x = 5 (# of nickels)
16-x = 11 (# of quarters)
================
Cheers,
Stan H.

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