1. at the Pittsburgh zoo, children ride a train for 25 cents, adults pay $1.00, and senior citizens pay 75 cents. On a given day, 1400 passengers paid a total of $740 for the rides. There were 250 more children riders than all other riders. Find the number of children, adult, and senior riders.
(answer: 825 children, 410 adults, 165 senior citizens)
2. Monica receives an $80,000 inheritance. She invests part of it in CDs (certificates of deposit) earning 6.7% APY (annual percentage yield), part in bonds earning 9.3% APY, and the remainder in a growth fund earning 15.6% APY. She invests three times as much in the growth fund as in the other two combined. How much does she have in each investment if she receives $10,843 interest the first year?
(answer: $14,500 CDs, $5500 bonds, $60,000 growth funds)
3. Morgan has $50,000 to invest and wants to receive $5000 interest the first year. He puts part in CDs earning 5.75% APY, part in bonds earning 8.7% APY, and the rest in a growth fund earning 14.6% APY. How much should he invest at each rate if he puts the least amount possible in the growth fund?
(answer: 0 CDs, $38,983.05 bonds, $11,016.95 growth fund)
4. Simpson's Drugstore needs to prepare a 40 L mixture that is 32% acid from three solutions: a 10% acid solution, a 25% acid solution, and a 50% acid solution. How much of each solution should be used if Simpson's wants to use as little of the 50% solution as possible?How would you solve these problems using systems? (or maybe matrices, i'm not sure which to use)?
Hi,
1. At the Pittsburgh zoo, children ride a train for 25 cents, adults pay $1.00, and senior citizens pay 75 cents. On a given day, 1400 passengers paid a total of $740 for the rides. There were 250 more children riders than all other riders. Find the number of children, adult, and senior riders.
(answer: 825 children, 410 adults, 165 senior citizens)
A + C + S = 1400
1A + .25C + .75S = 740
-A + C - S = 250
[ 1 _ 1 __1 __ 1400]
[ 1 _ .25 .75 _ 740 ] = A "_" used only for spacing
[-1 _ 1 _ -1 __ 250 ]
rref([A]) =
[1 . 0 . 0 . 410]
[0 . 1 . 0 . 825] = A "_" used only for spacing
[0 . 0 . 1 . 165]
2. Monica receives an $80,000 inheritance. She invests part of it in CDs (certificates of deposit) earning 6.7% APY (annual percentage yield), part in bonds earning 9.3% APY, and the remainder in a growth fund earning 15.6% APY. She invests three times as much in the growth fund as in the other two combined. How much does she have in each investment if she receives $10,843 interest the first year?
(answer: $14,500 CDs, $5500 bonds, $60,000 growth funds)
x + y + z = 80,000
.067x + .093y + .156z = 10,843
-3x - 3y + z = 0
[ 1 _____ 1 ____1 __ 80000 ]
[ .067 _ .093 _.156__ 10843 ] = A "_" used only for spacing
[ -3 ____ -3 ____1 ____ 0 . .]
rref([A]) =
[1 . 0 . 0 . 14500]
[0 . 1 . 0 . 5500 ] = A "_" used only for spacing
[0 . 0 . 1 . 60000]
3. Morgan has $50,000 to invest and wants to receive $5000 interest the first year. He puts part in CDs earning 5.75% APY, part in bonds earning 8.7% APY, and the rest in a growth fund earning 14.6% APY. How much should he invest at each rate if he puts the least amount possible in the growth fund?
(answer: 0 CDs, $38,983.05 bonds, $11,016.95 growth fund)
To put the least amount possible in the growth fund, the highest possible interest must be paid on all the non-growth fund investments. This means that all the non-growth fund money must go in bond because they pay a higher % rate than CDs.
So x = money in CDs = 0
y + z = 50,000
.087y + .146z = 5000
[1 ____ 1 50000]
[.087 .146 5000 ] = A "_" used only for spacing
[1 . 0 . 0 . 38,983.05]
[0 . 1 . 0 . 11,016.95] = A "_" used only for spacing
4. Simpson's Drugstore needs to prepare a 40 L mixture that is 32% acid from three solutions: a 10% acid solution, a 25% acid solution, and a 50% acid solution. How much of each solution should be used if Simpson's wants to use as little of the 50% solution as possible?
To use as little of the 50% solution as possible, the other solution has to have the highest % possible. So, none of the 10% acid solution will be used.
x = L of 10% solution = 0
y + z = 40
.25y + .50z = .32(40)
[1 __ 1 __ 40]
[.25 .50 12.8 ] = A "_" used only for spacing
[1 . 0 . 28.8]
[0 . 1 . 11.2] = A "_" used only for spacing
Use 28.8 L of 25% acid to mix with 11.2 L of 50% acid. %26lt;==ANSWER
I hope that helps!! :-)
Lit
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