Download Word Problems, Syst. Of Equations 1. Find the value of B so that the

Word Problems, Syst. Of Equations
1. Find the value of B so that the system of equations is inconsistent (no solutions):
4x + 2y = 10
10x + By = 20
B=5
2. The cost of produce floor tile includes a fixed cost of $400 and a variable cost of $1.25
per tile. The company charges a setup fee of $300 and $2 per tile. How many tile must be
sold before the company makes a profit? (134)
Cost = set up + tile cost; Profit = setup fee + tile charge; breakeven is when cost = profit
Cost = 400 + 1.25x, where x is the number of tile
Profit = 300 + 2x
need 400 + 1.25x = 300 + 2x; 100 = 0.75x, x = 100/0.75 = 133.3 tiles
3. The sum of twice one number plus a second number is 14. The first number minus the
second number is 4. Find the numbers.
2n + m = 14, n – m = 4; From 2nd eq n = m + 4, put in 1st, 2(m+4) + m = 14
3m + 8 = 14, m = 2, n = 6
4. Find two numbers whose sum is 213 if one number is twice the other number.
n +m = 213, 2n = m
n + 2n = 213, 3n = 213, n = 71
n = 71, m = 142
5. Solve for x and y in terms of a, b, and c. Assume a, b, and c are all non-zero.
ax + by = c
2ax – by = 2c
Add two equations, and get 3ax = 3c, therefore, x = c/a
substitute into 1st equation: a(c/a) + by = c, or c + by = c, y = 0
check; a(c/a) + b(0)= c OK, 2a(c/a) – b(0) = 2c or 2c = 2c OK.
6. Hilda invested part of her $25000 in savings bonds at 7% simple interest and the rest in
stocks at 8% simple interest. If she receives $1900 a year in interest, how much did she
invest in each account?
Let B be the amount in bonds and S the amount in stocks
S + B = 25,000, Interest = 1900 = 0.07B + 0.08 S
From 1st equation, S = 25,000 – B, subst into 2nd: 1900 = 0.07B + 0.08(25,000 – B) =
-0.01B + 2000, B = 100/0.01 = $10,000, S = $15,000
7. Tickets to a theatre cost $8 for students and $10 for nonstudents. They sold 390 tickets
and made $3270. How many student tickets were sold?
S = student tickets, N = non-student
S+N=390, 8S + 10N = 3270. From 1st equation, N = 390-S. Subst into 2nd,
8S + 10(390-S) = 3270, -2S + 3900 = 3270, 2S = 630, S = 315 student tickets
8. The perimeter of a rectangular garden is 650 meters. If the length is 75 meters more than
the width, what are the dimensions of the garden?
P = 2L + 2W, L = W + 75. P = 2(W+75) + 2W = 4W + 150 = 650, 4W = 500, W =125m
L = 200m
9. A baker wants to mix a 60% sugar solution with a 30% sugar solution to obtain 10 quarts
of a 51% sugar solution. How much of the 30% solution will the baker use?
Name
60% sol
30% sol
51% sol
Amount
x
y
10 qt
Concentration
60%
30%
51%
Sugar
0.6x
0.3y
5.1
x + y = 10, 0.6x + 0.3y = 5.1 or 6x + 3y = 51
from 1st equation, x = 10-y; subst into 2nd: 6(10-y) + 3y = 51 or 60 -3y = 51; 3y = 9 or
y = 3; needs 3 qt of 30% solution