The system of equations is
n + d = 27
n + 5d = 55
Step-by-step explanation:
The given is:
- Kiran has 27 nickels and quarters in his pocket
- They worth a total of $2.75
- We need to write a system of equations to represent the relationships between the number of nickels n, the number of quarters d, and the dollar amount in this situation
∵ The number of nickles is n
∵ The number of quarters is d
∵ There are 27 nickles and quarters
∴ n + d = 27 ⇒ (1)
∵ 1 nickel = 5 cents
∵ 1 quarter = 25 cents
- Multiply n by 5 and d by 25 to find their value
∴ They worth = 5n + 25d
∵ They worth a total of $2.75
- Chang the dollar to cent
∵ 1 dollar = 100 cents
∴ $2.75 = 2.75 × 100 = 275 cents
- Equate their value by 275
∴ 5n + 25d = 275
- Simplify it by divide each term by 5
∴ n + 5d = 55 ⇒ (2)
The system of equations is
n + d = 27
n + 5d = 55
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Answer:
x = 15°
Step-by-step explanation:
<u>We are given;</u>
sin(2x + 7) = cos(4x - 7)
We are required to solve for the value of x
- We need to know that for complementary angles;
Sin θ = Cos (90-θ) where, θ and 90-θ are complementary angles.
- Complementary angles are angles that add to 90°
- Therefore;
(2x +7) + (4x - 7) = 90
6x = 90
x = 15°
Therefore, the value of x is 15°
Answer:
£265
Step-by-step explanation:
Total fraction of money spent= 
= 
Actual money spent = * £636
= £371
Money he has left = £(636 - 371)
= £265
Answer:
<u>The percentage loss per gallon is 23.17%</u>
Step-by-step explanation:
Original price per gallon = $ 2.59
Discounted price per gallon = $ 1.99
Now, let's calculate the percentage loss per gallon, using the Direct Rule of Three, as follows:
Price Percentage
2.59 100
1.99 x
*****************************
2.59 * x = 1.99 * 100
2.59x = 199
x = 199/2.59
x = 76.83
Percentage loss = 100 - 76.83
<u>Percentage loss = 23.17%</u>
Answer: $13
Step-by-step explanation:
To determine the solution arithmetically in two steps, first divide 68.25 by 3 and then subtract 9.75 from the result. To determine the solution algebraically, set up and solve the equation 3(x+9.75)=68.25. Each friend paid $13 for dinner.
