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2 years ago

Using the least number of coins how many quarters, dimes, nickels, and pennies to make $1.74

Mathematics

1 answer:

SpyIntel [72]2 years ago

4 0

Let's use our largest amount (quarter) to see how many can fit evenly into 1.74.

1.74/0.25 = 6.96
The most quarters that can fit into $1.74 is 6.

---Multiply $0.25 by 6 = $1.50

---Subtract $1.50 from $1.74 = $0.24

---We need to use the rest of the coins to fill up $0.24.

Now let's use our second largest amount (dime) to see how many can fit evenly into 0.24.

0.24/0.10 = 2.4
The most dimes that can fit into $0.24 is 2.

---Multiply $0.10 by 2 = $0.20

---Subtract $0.20 from $0.24 = $0.04

No nickels can fit into $0.04, because they are worth $0.05.

We can use our least amount (pennies) to fill in the $0.04 remaining.

Your answer is 6 quarters, 2 dimes, and 4 pennies.

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2 years ago

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3 years ago

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Artyom0805 [142]

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2 years ago

Solve the following pair of equations simultaneously.

Alchen [17]

Answer:

No solutions.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS
Equality Properties

Algebra I

Solving systems of equations using substitution/elimination
Solving systems of equations by graphing
Expanding
Finding roots of a quadratic
Standard Form: ax² + bx + c = 0
Quadratic Formula: $x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$

Step-by-step explanation:

Step 1: Define systems

2x - y = 9

4x² + 3y² - 2x + y = 16

Step 2: Rewrite systems

2x - y = 9

Subtract 2x on both sides: -y = 9 - 2x
Divide -1 on both sides: y = 2x - 9

Step 3: Redefine systems

y = 2x - 9

4x² + 3y² - 2x + y = 16

Step 4: Solve for x

Substitution

Substitute in y: 4x² + 3(2x - 9)² - 2x + (2x - 9) = 16
Expand: 4x² + 3(4x² - 36x + 81) - 2x + (2x - 9) = 16
Distribute 3: 4x² + 12x² - 108x + 243 - 2x + 2x - 9 = 16
Combine like terms: 16x² - 108x + 234 = 16
Factor GCF: 2(8x² - 54x + 117) = 16
Divide 2 on both sides: 8x² - 54x + 117 = 8
Subtract 8 on both sides: 8x² - 54x + 109 = 0
Define variables: a = 8, b = -54, c = 109
Resubstitute: $x=\frac{54\pm\sqrt{(-54)^2-4(8)(109)} }{2(8)}$
Exponents: $x=\frac{54\pm\sqrt{2916-4(8)(109)} }{2(8)}$
Multiply: $x=\frac{54\pm\sqrt{2916-3488} }{16}$
Subtract: $x=\frac{54\pm\sqrt{-572} }{16}$

Here we see that we start to delve into imaginary roots. Since on a real number plane, we do not have imaginary roots, there would be no solution to the systems of equations.

Step 5: Graph systems

We can verify our results.

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2 years ago

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tatyana61 [14]

60 mph would be the correct answer!
Brainilest please! :)

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2 years ago

Read 2 more answers