Unit 1C/2A Matrices TEST REVIEW KEY
Solve for x and y
1)
=
2)
x = 1.5, y = 3
=
x = 1, y = 1
3)
4)
X = 15, y = 4
x = -9, y = 7
Evaluate the following if possible using these given matrices:
E=
H=
5. E + F
F=
G=
J=
E = 3x2, F = 2x3, G = 2x2
K=
6. EF
7. FE
Not possible
H = 3x2, J = 1x3, K = 3x1
8. H2
9. G2
10. FK
not possible
Write the matrix equation for each system and solve, if possible:
x = 20, y = 10
=
12.
x = 5, y = 4
=
x = 4, y = 3, z = 214
=
x = -1, y = -2.5, z = 3.5
=
15. A florist is making 5 identical bridesmaid bouquets for a wedding. She has $610 to
spend (including tax) and wants 24 flowers for each bouquet. Roses cost $6 each, tulips
cost $4 each, and lilies cost $3 each. She wants to have twice as many roses as the
other 2 flowers combined in each bouquet. How many roses, tulips, and lilies are in
each bouquet? X = # roses, y = # tulips, z = # lilies
X = 16
y=2
z=6
=
16. Scott is in charge of purchasing a variety of tickets to a baseball game to be given
to employees who met or exceeded their sales quotas for the past month. There are 3
types of tickets available for the game at a cost of $25 a piece, $35 a piece, or $50 a
piece. He knows that he needs to buy 40 tickets in all and can spend $1670. He wants to
buy twice as many $35 tickets as $25 tickets. How many of each type of ticket should he
buy? X = # of $25 tickets y = # of $35 tickets z = # of $50 tickets
x=6
y = 12
z = 22
17. Carmel put her $5000 earnings into three different accounts. The accounts paid
simple annual interest of 8%, 10%, and 7%, respectively. The total interest at the end
of one year was $405. If Carmel invested $500 more at 10% than at 8%, find the
amount she invested in each account. x = amt 8%, y = amt 10%, z = amt 7%
x = $1000, y = $1500, z = $2500
18. John inherited $25,000 and invested part of it in a money market account, part in
municipal bonds, and part in a mutual fund. After one year, he received a total of
$1,620 in simple interest from the three investments. The money market paid 6%
annually, the bonds paid 7% annually, and the mutually fund paid 8% annually. There
was $6,000 more invested in the bonds than the mutual funds. Find the amount John
invested in each category. X = amt money mkt, y = amt bonds, z = amt mutual
x = $15000, y = $8000, z = $2000
19. The sum of the digits of a three-digit number is 12. The tens digit is 2 less than the
hundreds digit, and the units digit is 4 less than the sum of the other two digits. What is
the number? X = hundreds digit, y = tens digit, z = units digit
x = 5, y = 3, z = 4; the number is 534
20. The sum of three numbers is 16. The largest number is equal to the sum of the
other two, and 3 times the smallest number is 1 more than the largest. Find the three
numbers. X = largest #, y = middle #, z = smallest #
x = 8, y = 5, z = 3
For fun: Bill, a very observant yet clumsy man with a wad of cash in his hands, was just
leaving from getting his wash done at the local laundry mat when he bumped into
another person holding his own wad of cash. Currency flew everywhere. The other man
began to get very irate with Bill; he wanted his money. Bill thought back and
remembered entering with 150 dollars in coins and bills. He thought back some more
and recalled spending all $9 worth of coins he had been carrying and not carrying any
bills larger than a fifty. He recalled counting 11 bills, having a total of 5 Washington DC
monuments on the back sides of the bills, 3 pictures of presidents with beards, and 92
letters worth of presidential last names. Even with all of that memory, he failed to
remember what bills he had. Find the correct denomination of bills Bill was carrying.
On your own, for fun.