SOLUTION: Solve by writing a system of equation.
a. Anne Matie has 52 coins in dimes and quarters which are worth $6.25. How many of each coin does she have.
b. John has a total of 9 s
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Question 82979: Solve by writing a system of equation.
a. Anne Matie has 52 coins in dimes and quarters which are worth $6.25. How many of each coin does she have.
b. John has a total of 9 stamps, which consists of 25 cent and 2 cent stamps. His stamps have a value of $1.10. How many of each stamp does he have?
c. It takes 4 h for a boat to travel 56 mil downstream. The same boat can 36 mil upstream in 6 hrs. Find the rate of speed of the boat in still water and the rate of the current
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Solve by writing a system of equation.
a. Anne Matie has 52 coins in dimes and quarters which are worth $6.25. How many of each coin does she have.
:
The number of coins equation
d + q = 52
d = 52-q; use for substitution
:
The $amt equation:
.10d + .25q = 6.25
:
Substitute (52-q) for d in the above equation:
.10(52-q) + .25q = 6.25
5.2 - .10q + .25q = 6.25
+.15q = 6.25 - 5.2
.15q = 1.05
q = 1.05/.15
q = 7 quarters
and
d = 52 -7 = 45 dimes
:
Check .10(45) + .25(7) = 6.25
:
:
b. John has a total of 9 stamps, which consists of 25 cent and 2 cent stamps. His stamps have a value of $1.10. How many of each stamp does he have?
:
Let x = no. of 25 cent stamps
Then (9-x) = no. of 2 cent stamps
:
.25x + .02(9-x) = 1.10
.25x + .18 - .02x = 1.10
.23x = 1.10 - .18
.23x = .92
x = .92/.23
x = 4 ea 25 cent stamps
Obviously that leave 5 ea 2 cent stamps
;
Check solution:
.25(4) + .02(5) = 1.10
:
:
c. It takes 4 h for a boat to travel 56 mil downstream. The same boat can 36 mil upstream in 6 hrs. Find the rate of speed of the boat in still water and the rate of the current
:
Let x = speed of the boat in still water; Let y = speed of the current:
Then:
Speed upstream: (x-y)
Speed downstream: (x+y)
:
Write two distance equations; dist = time * speed
4(x + y) = 56
6(x - y) = 36
:
Divide the 1st equation by 4 and the 2nd equation by 6 and you have:
x + y = 14
x - y = 6
-------------adding eliminates y; find x
2x + 0 = 20
x = 20/2
x = 10 mph in still water
:
Find y using x - y = 6
10 - y = 6
y = 4 mph is the current
:
Check solutions:
4(10+4) = 52
6(10-4) = 36
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