Saturday, October 31, 2015
Solving simultaneous equations
Here is a link to practice problems for simultaneous equations. The coin problems all use elimination instead of substitution. Here are the same coin problems using substitution, with the answers in the comment below.
a) 100 coins, all quarters and pennies, total = $13.72
b) 100 tickets, all children ($6) and adult ($12), total =$912
c) 100 coins, all quarters and nickels, total = $8.20
d) 100 coins, all dimes and pennies, total = $3.79
e) 100 coins, all dimes and nickels, total = $7.85
f) 100 coins, all quarters and dimes, total = $14.65
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a) 100 coins, all quarters and pennies, total = $13.72
q + p = 100
25q + p = 1372
Use the first equation to get p = 100 - q
The second equation becomes
25q + 100 - q = 1372
24q + 100 = 1372
24q = 1272
q = 1272/24 = 53
p = 100 - 53 = 47
b) 100 tickets, all children ($6) and adult ($12), total =$912
c + a = 100
6c + 12a = 912
Use the first equation to get c = 100 - a
The second equation becomes
6(100 - a) + 12a = 912
600 - 6a + 12a = 912
600 + 6a = 912
6a = 312
a = 312/6 = 52
c = 100 - 52 = 48
c) 100 coins, all quarters and nickels, total = $8.20
q + n = 100
25q + 5n = 820
Use the first equation to get n = 100 - q
The second equation becomes
25q + 5(100 - q) = 820
25q + 500 - 5q = 820
20q + 500 = 820
20q = 320
q = 320/20 = 16
c = 100 - 16 = 84
d) 100 coins, all dimes and pennies, total = $3.79
d + p = 100
10d + p = 379
Use the first equation to get p = 100 - d
The second equation becomes
10d + 100 - d = 379
9d + 100 = 379
9d = 279
d = 279/9 = 31
p = 100 - 31 = 69
e) 100 coins, all dimes and nickels, total = $7.85
d + n = 100
10d + 5n = 785
Use the first equation to get n = 100 - d
The second equation becomes
10d + 5(100 - d) = 785
10d + 500 - 5d = 785
5d + 500 = 785
5d = 285
d = 285/5 = 55
n = 100 - 55 = 45
f) 100 coins, all quarters and dimes, total = $14.65
q + d = 100
25q + 10d = 1465
Use the first equation to get d = 100 - q
The second equation becomes
25q + 10(100 - q) = 1465
25q + 1000 - 10q = 1465
15q + 1000 = 1465
15q = 465
q = 465/15 = 31
d = 100 - 31 = 69
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