Thank you for visiting A boy has 11 coins in dimes and quarters Their value is tex 1 70 tex How many of each does he have Which of. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Sure! To solve this problem, we can use one of the equations provided to find out how many dimes and quarters the boy has.
Let's break this down:
1. Define the variables:
- Let [tex]\( x \)[/tex] be the number of dimes.
- Therefore, [tex]\( 11 - x \)[/tex] will be the number of quarters since there are 11 coins in total.
2. Assign values to the coins:
- Dime is worth [tex]$0.10.
- Quarter is worth $[/tex]0.25.
3. Set up an equation for the total value:
- The value of [tex]\( x \)[/tex] dimes is [tex]\( 0.10x \)[/tex].
- The value of [tex]\( 11 - x \)[/tex] quarters is [tex]\( 0.25 \times (11 - x) \)[/tex].
- The total value of these coins is [tex]$1.70, which leads to the equation:
\[
0.10x + 0.25(11 - x) = 1.70
\]
4. Simplify and solve the equation:
- Start by distributing the $[/tex]0.25:
[tex]\[
0.10x + 0.25 \times 11 - 0.25x = 1.70
\][/tex]
[tex]\[
0.10x + 2.75 - 0.25x = 1.70
\][/tex]
- Combine like terms:
[tex]\[
(0.10 - 0.25)x + 2.75 = 1.70
\][/tex]
[tex]\[
-0.15x + 2.75 = 1.70
\][/tex]
- Subtract 2.75 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
-0.15x = 1.70 - 2.75
\][/tex]
[tex]\[
-0.15x = -1.05
\][/tex]
- Divide both sides by -0.15 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-1.05}{-0.15}
\][/tex]
[tex]\[
x = 7
\][/tex]
5. Conclusion:
- The boy has 7 dimes.
- Since he has 11 coins in total, the number of quarters is [tex]\( 11 - x = 11 - 7 = 4 \)[/tex].
So, the boy has 7 dimes and 4 quarters. This setup is represented by the third equation provided: [tex]\( 0.10x + 0.25(11-x) = 1.70 \)[/tex].
Let's break this down:
1. Define the variables:
- Let [tex]\( x \)[/tex] be the number of dimes.
- Therefore, [tex]\( 11 - x \)[/tex] will be the number of quarters since there are 11 coins in total.
2. Assign values to the coins:
- Dime is worth [tex]$0.10.
- Quarter is worth $[/tex]0.25.
3. Set up an equation for the total value:
- The value of [tex]\( x \)[/tex] dimes is [tex]\( 0.10x \)[/tex].
- The value of [tex]\( 11 - x \)[/tex] quarters is [tex]\( 0.25 \times (11 - x) \)[/tex].
- The total value of these coins is [tex]$1.70, which leads to the equation:
\[
0.10x + 0.25(11 - x) = 1.70
\]
4. Simplify and solve the equation:
- Start by distributing the $[/tex]0.25:
[tex]\[
0.10x + 0.25 \times 11 - 0.25x = 1.70
\][/tex]
[tex]\[
0.10x + 2.75 - 0.25x = 1.70
\][/tex]
- Combine like terms:
[tex]\[
(0.10 - 0.25)x + 2.75 = 1.70
\][/tex]
[tex]\[
-0.15x + 2.75 = 1.70
\][/tex]
- Subtract 2.75 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
-0.15x = 1.70 - 2.75
\][/tex]
[tex]\[
-0.15x = -1.05
\][/tex]
- Divide both sides by -0.15 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-1.05}{-0.15}
\][/tex]
[tex]\[
x = 7
\][/tex]
5. Conclusion:
- The boy has 7 dimes.
- Since he has 11 coins in total, the number of quarters is [tex]\( 11 - x = 11 - 7 = 4 \)[/tex].
So, the boy has 7 dimes and 4 quarters. This setup is represented by the third equation provided: [tex]\( 0.10x + 0.25(11-x) = 1.70 \)[/tex].
Thank you for reading the article A boy has 11 coins in dimes and quarters Their value is tex 1 70 tex How many of each does he have Which of. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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