Tanya has ten bills in her wallet . She has a total of $ 40. If she has one more $ 5 bill than $ 10 bills…?
1. Tanya has ten bills in her wallet . She has a total of $ 40. If she has one more $ 5 bill than $ 10 bills, and two more $ 1 bills than $ 5 bills , how many of each does she have ?
And:
2. Mario bought .44 worth of stamps at the post office. He bought 10 more 4-cent stamps than 19-cent stamps. The number of 32-cent stamps was three times the number of 19-cent stamps. He also bought two $ 1 stamps. How many of each kind of stamp did he purchase?
3 . Mr. Abernathy purchases a selection of wrenches for his shop. His bill is $ 78. He buys the same number of $ 1.50 and $ 2.50 wrenches , and half that many of wrenches . The number of wrenches is one more than the number of wrenches. How many of each did he purchase?
4. A clerk at the Dior Department Store receives $ 15 in change for her cash drawer at the start of each day. She receives twice as many dimes as fifty-cent pieces, and the same number of quarters as dimes. She has twice as many nickels as dimes and a dollar’s worth of pennies. How many of each kind of coin does she receive?
5. A collection of 36 coins consists of nickels, dimes, and quarters. There are three fewer quarters than nickels and six more dimes than quarters. How many of each kind of coin are there?
6. The cash drawer of the market contains $ 227 in bills. There are six more $ 5 bills than $ 10 bills. The number of $ 1 bills is two more than 24 times the number of $ 10 bills. How many bills of each kind are there?
7. Terry bought some gum and some candy. The number of packages of gum was one more than the number of mints. The number of mints was three times the number of candy bars. If gum was 24 cents a packages, mints were 10 cents each, and candy bars were 35 cents each, how many of each did he get for .72?
8. Jose Ramirez has to buy groceries. He bought milk at .95 a carton, bread at .39 a loaf, breakfast cereal at .00 a box and meat at .39 a pound. He bought twice as many cartons of milk as loaves of bread and one more package of cereal than loaves of bread. He also bought the same number of pounds of meat as packages of cereal. How many of each item did be buy if he received .25 in change?
Its all Coin Problems but I'm not sure how to do them so if you could show me how to get the answers that would be great
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April 27th, 2009 at 2:24 pm
1. x = # of $5 bills, y = # of $10 bills and z = # $1 bills.
then you have:
5x + 10y + z = 40 (3)
x = y + 1 (1)
z = x + 2 (2)
let's rarrange equation 1 to get y in terms of x:
y = x - 1 (4)
now substitute equations 2 and 4 in number 3:
5x + 10( x - 1 ) + x + 2 = 40
5x + 10x - 10 + x = 38
16x = 48
x = 3 now substitute in equations 2 and 4:
z = 5
y = 2.
Hence Tanya has 3 $5 bills, 2 $10 bills and 5 $1 bills.
2. a = 4 cent stamps
b = 19 cent stamps
c = 32 cent stamps
d = $1 stamps = 100 cent stamps ( to avoid confusion )
4a + 19b + 32c + 100d = 2144
a = b + 10
c = 3b
d = 2
4(b + 10) + 19b + 32(3b) +100(2) = 2144
4b + 40 + 19b + 96b + 200 = 2144
23b + 96b + 240 = 2144
119b = 1904
b = 16, a = 26, c = 48.
That's 26 4-cent stamps, 16 19-cent stamps, 48 32-cent stamps and 2 $1 stamps
3. a = $1.50 wrenches
b = $2.50 wrenches
c = $4.00 wrenches
d = $3.00 wrenches
1.50a + 2.50b + 4.00c + 3.00d = 78
a = b = 2c
c = a/2 = b/2
d = c + 1
so let's express the first equation in terms of c:
1.50(2c) + 2.50(2c) + 4.00c + 3.00(c + 1) = 78.00
3.00c + 5.00c + 4.00c + 3.00c + 3.00 = 78.00
15.00c = 75.00
c = 5 therefore a = b = 10 and d well d = 6.
That's 10 $1.50 wrenches, 10 $2.50 wrenches, 5 $4.00 wrenches and 6 $3.00 wrenches.
4. a = pennies
b = nickels
c = dimes
d = quarters
e = 50 cent pieces
so:
a + 5b + 10c + 25d + 50e = 1500
e = 2c = 2d
c = d
2b = c, b = c/2, b = d/2
a = 100
so:
lets express in terms of d:
100 + 5(d/2) + 10d + 25d + 50(2d) = 1500
100 + 5d/2 + 10d + 25d + 100d = 1500
5d/2 + 135d = 1500 - 100
5d/2 + 270d/2 = 1400
275d/2 = 1400
275d = 2800
d = 2800/275 = 112/11
e = 224/11
a = 100
b = 112/22 = 56/11
c = 112/11
5. x = nickles, y = dimes, z = quarters
x + y + z = 36
z - 3 = x
x = z - 3
y + 6 = z,
y = z - 6
we have x and y in terms of z now substitute:
z - 3 + z - 6 + z = 36
3z = 45
z = 15
y = 15 - 6
y = 9
x = 15 - 3
x = 12
12 nickles, 9 dimes and 15 quarters.
6. m = $5, n = $10 and p = $1
5m + 10n + p = 227
6 + m = n
p = 2 + 24n
m = n - 6
substitute in terms of n:
5(n - 6) + 10n + 2 + 24n = 227
5n - 30 + 10n + 2 + 24n = 227
15n + 24n = 227 + 28
39n = 255
n = 255/39 = 85/13
m = 85/13 - 6 = (85 -78)/13 = 7/13
p = 2 + 24(85/13) = 2040/13 + 26/13 = 2066/13
7. x = gum, y = mint, z = candy bar
x = y + 1
y = 3z
z = y/3
0.24x + 0.10y + 0.35z = 5.72
we have x and z in terms of y now subsitute:
0.24(y + 1) + 0.10y + 0.35(y/3) = 5.72
.24y + .24 + .10y + .35y/3 = 5.72
0.34y + .35y/3 = 5.72 - .24
(1.02y + 0.35y)/3 = 5.48
1.37y/3 = 5.48
y = (5.48)(3)/(1.37)
y = 12
x = 13
z = 4
8. g = milik cartons,
h = loafs of bread
i = boxes of cereal
j = pounds of meat
2g = h, g = h/2
i + 1 = h, i = h - 1
i = j, j = h - 1
1.95g + 2.39h + 3.00i + 5.39j = 50.00 - 12.25
Let's express in terms of h:
1.95(h/2) + 2.39h + 3.00(h - 1) + 5.39(h - 1) = 50.00 - 12.25
1.95h/2 + 2.39h + 3.00h - 3.00 + 5.39h - 5.39 = 37.75
(1.95h + 4.78h + 6.00h +10.78h)/2 = 37.75 + 3.00 + 5.39
23.51h/2 = 46.14
h = 46.14(2)/23.51
h = 92.28/23.51
g = 92.28/47.02
i = (92.28 - 23.51)/23.51 = 68.77/23.51
j = (92.28 - 23.51)/23.51 = 68.77/23.51
There you go