Question

1. select all the equations that have the same solution as the equation 3x - 12 = 24. a. 15x - 60 = 120 b. 3x = 12 c. 3x = 36 d. x - 4 = 8 e. 12x - 12 = 24 3. jada has a coin - jar containing n nickels and d dimes worth a total of $3.65. the equation 0.05n + 0.1d = 3.65 is one way to represent this situation. which equation is equivalent to the equation 0.05n + 0.1d = 3.65? a. 5n + d = 365

Explanation:

Step1: Solve the equation $3x - 12=24$

Add 12 to both sides: $3x=24 + 12$, so $3x=36$. Then divide both sides by 3, we get $x = 12$.

Step2: Check option A

For $15x-60 = 120$, add 60 to both sides: $15x=120 + 60=180$. Divide both sides by 15, $x=\frac{180}{15}=12$.

Step3: Check option B

For $3x = 12$, divide both sides by 3, $x = 4
eq12$.

Step4: Check option C

We already got from solving the original equation that $3x=36$ has solution $x = 12$.

Step5: Check option D

For $x - 4=8$, add 4 to both sides, $x=8 + 4=12$.

Step6: Check option E

For $12x-12 = 24$, add 12 to both sides: $12x=24+12 = 36$. Divide both sides by 12, $x = 3
eq12$.

Step7: Solve the coin - value equation

For $0.05n+0.1d=3.65$, multiply each term by 100 to clear the decimals. We get $5n + 10d=365$, divide each term by 10 gives $0.5n + d=36.5$, multiply by 10 again gives $5n + d=365$.

Answer:

1. A. $15x - 60 = 120$, C. $3x = 36$, D. $x - 4 = 8$
2. A. $5n + d = 365$