Problem 1 :
The length of a rectangle is equal to triple the width. Which system of equations can be used to find the dimensions of the rectangle if the perimeter is 86 centimeters?
Problem 2 :
At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk $5.15. Which pair of equations can be used to determine t, the cost of a taco, and m, the cost of a small glass of milk?
Problem 3 :
The Frosty Ice-Cream Shop sells sundaes for $2 and banana splits for $3. On a hot summer day, the shop sold 8 more sundaes than banana splits and made $156.
Problem 4 :
Chase and Sara went to the candy store. Chase bought 5 pieces of fudge and 3 pieces of bubble gum for a total of $5.70. Sara bought 2 pieces of fudge and 10 pieces of bubble gum for a total of $3.60. Which system of equations could be used to determine the cost of 1 piece of fudge, f, and 1 piece of bubble gum, g?
Problem 5 :
At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, m, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?
Problem 6 :
The price, e, of an entertainment system at Extreme Electronics is $220 less than twice the price, u, of the same system at Ultra Electronics. The difference in price between the system at Extreme Electronics and Ultra Electronics is $175. Which system of linear equations can be used to determine the price of the system at each store?
1. Answer
Let l and w be length and width respectively.
l = 3w
2(l + w) = 85
l - 3w = 0 ---> (1)
2l + 2w = 85 ---> (2)
2(1) - (2) :
w = 85/8
w = 10.625 cm
Substitute w = 10.625 into (1)
l - 3(10.625) = 0
l - 31.875 = 0
l = 31.875 cm
Therefore, the length and width are 31.875 cm and 10.625 cm.
2. Answer
Let t and m be the cost of taco and cost of milk.
t + m = 2.10 ---> (1)
2t + 3m = 5.15 ---> (2)
2(1) - (2) :
m = 0.95
Substitute m = 0.95 into (1)
t + 0.95 = 2.10
t = 2.10 - 0.95
t = 1.15
Therefore, the cost of taco and milk are 1.15 and 0.95.
3. Answer
Let s and b be the sundaes and banana.
2s + 3b = 156 ---> (1)
s = b + 8
s - b = 8 ---> (2)
(1) + 3(2) :
s = 36
Substitute s = 36 into (2)
36 - b = 8
-b = 8 - 36
-b = -28
b = 28
4. Answer
Let f and g be the fudge and bubble gum.
5f + 3g = 5.70 ---> (1)
2f + 10g = 3.60 ---> (2)
2(1) - 5(2) :
g = 6.6/44
g = 0.15
Substitute g = 0.15 into (1)
5f + 3(0.15) = 5.70
5f + 0.45 = 5.70
5f = 5.25
f = 1.05
Therefore, cost of fudge and bubble gum are 1.05 and 0.15.
5. Answer
Let m and n be the math text book and novel.
m + n = 54 ---> (1)
m = 3n + 8
m - 3n = 8 ---> (2)
(1) - (2) :
n = 46/4
n = 11.5
Substitute n = 11.5 into (1)
m + 11.5 = 54
m = 54 - 11.5
m = 42.5
6. Answer
Let e and u be the Extreme electronics and Ultra electronics.
e - 2u = -220 ---> (1)
e - u = 175 ---> (2)
(1) - (2) :
u = 395
Substitute u = 395 into (2)
e - 395 = 175
e = 570
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM