Answer: Ali would need to drive 350 miles for the two plans to cost the same.
Step-by-step explanation:
This question can be solved by creating two equations using the information supplied in the question and then solving these simultaneously.
Let the cost be C.
Let the number of miles be M.
Let the initial payment be i.
Let the rate per mile driven be R.
Plan 1:
C = i+R×M
C = 70+0.60M ... equation 1
Plan 2:
C = i+R×M
C = 0+0.80M
C = 0.80M ...equation 2
Substituting equation 2 into equation 1:
0.80M = 70+0.60M
0.80-0.60M = 70
0.20M = 70
M = 70/0.20
M = 350 miles
2/10 because there are 10 cards and there are 5 circles and 3 triangles
Answer:
1/52
Step-by-step explanation:
2 to the fourth is 16, and 6 to the second is 36. However, since it's a negative exponent, you'd have to move it down to to the bottom of the fraction, creating 1/16+36, which makes 1/52.
Kim's Loan:
Let A = amount borrowed from bank A.
Let B = amount borrowed from bank B.
The total loan is $55,000.
Therefore
A + B = 55000 (1)
Bank A charges 8% interest. The interest after 1 year is 0.08A.
Bank B charges 11% interest. The interest after 1 year is 0.11B.
Total interest after 1 year is $5,000.
Therefore
0.08A + 0.11B = 5000 (2)
From (1), obtain
B = 55000 - A (3)
Substitute (3) into (2).
0.08A + 0.11(55000 - A) = 5000
0.08A + 6050 - 0.11A = 5000
-0.03A = -1050
A = -1050/-0.03 = 35000
Answer: Kim borrowed $35,000 from bank A.
Jack's Loan.
A = loan from bank A.
B = loan from bank B.
The total loan is $10,000.
Therefore
A + B = 10000 (4)
Bank A charges 5% interest and bank B charges 6% interest.
Total interest after 1 year is $530, therefore
0.05A + 0.06B = 530 (5)
From (4), obtain
B = 10000 - A (6)
Substitute (6) into (5).
0.05A + 0.06(10000 - A) = 530
0.05A + 600 - 0.06A = 530
-0.01A = -70
A = -70/-0.01 = 7000
Answer: Jack borrowed $7,000 from bank A.
