Certainly! Here's a clear explanation and the steps to form the equation and solve it: A) To write an equation, we need to define the variables for the number of dimes and quarters. Let's call the number of dimes 'd'. Since the number of quarters is 8 less than the number of dimes, we can call the number of quarters 'd - 8'. Now we know that the value of a dime is $0.10 and the value of a quarter is $0.25. To find the total value of the dimes and quarters, we multiply the number of each coin by its value and add these amounts together to equal $4.30. The equation representing the total value is: 0.10d (value of the dimes) + 0.25(d - 8) (value of the quarters) = $4.30 B) To solve for the number of dimes, clear the decimals from the equation by multiplying every term by 100: 10d + 25(d - 8) = 430 Now distribute the 25 through the parentheses: 10d + 25d - 200 = 430 Combine like terms: 35d - 200 = 430 Add 200 to both sides to solve for 35d: 35d = 630 Now divide by 35 to solve for d: d = 630 / 35 d = 18 There are 18 dimes in the jar.

Question

Certainly! Here's a clear explanation and the steps to form the equation and solve it: A) To write an equation, we need to define the variables for the number of dimes and quarters. Let's call the number of dimes 'd'. Since the number of quarters is 8 less than the number of dimes, we can call the number of quarters 'd - 8'. Now we know that the value of a dime is $0.10 and the value of a quarter is $0.25. To find the total value of the dimes and quarters, we multiply the number of each coin by its value and add these amounts together to equal $4.30. The equation representing the total value is: 0.10d (value of the dimes) + 0.25(d - 8) (value of the quarters) = $4.30 B) To solve for the number of dimes, clear the decimals from the equation by multiplying every term by 100: 10d + 25(d - 8) = 430 Now distribute the 25 through the parentheses: 10d + 25d - 200 = 430 Combine like terms: 35d - 200 = 430 Add 200 to both sides to solve for 35d: 35d = 630 Now divide by 35 to solve for d: d = 630 / 35 d = 18 There are 18 dimes in the jar.

Mathematics · Middle School · Thu Feb 04 2021

llm

Answered on Tue Nov 21 2023

: A) To create an equation, let’s assign variables for the number of dimes and quarters. Let's say the number of dimes is represented by the variable 'd', and the number of quarters will be 8 less than the number of dimes, so we can denote it as 'd - 8'.

Given the value of a dime is 10 cents or $0.10, and the value of a quarter is 25 cents or $0.25, we can set up the equation for their total value. The equation should represent that the total value of the dimes and quarters combined equals $4.30.

This gives us the equation: \[ 0.10d + 0.25(d - 8) = 4.30 \]

B) Now, we have to solve for 'd', which is the number of dimes:

First, distribute the 25 cents to each term inside the parentheses: \[ 0.10d + 0.25d - 2.00 = 4.30 \]

Combine the like terms (0.10d + 0.25d): \[ 0.35d - 2.00 = 4.30 \]

Add $2.00 to both sides to isolate the term with the variable 'd': \[ 0.35d = 4.30 + 2.00 \] \[ 0.35d = 6.30 \]

Now, divide both sides by 0.35 to solve for 'd': \[ d = 6.30 / 0.35 \] \[ d = 18 \]

Therefore, there are 18 dimes in the jar.

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