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! Let's solve this problem step by step.
We need to find out how many dimes and quarters the boy has, given that:
1. He has a total of 11 coins.
2. The total value of these coins is [tex]$1.70.
We can define:
- \( d \): the number of dimes.
- \( q \): the number of quarters.
From the information given, we can set up two equations:
1. The total number of coins equation:
\( d + q = 11 \)
2. The total value equation in dollars (remember, a dime is worth $[/tex]0.10 and a quarter is worth $0.25):
[tex]\( 0.10d + 0.25q = 1.70 \)[/tex]
Now, let's use these equations to solve for [tex]\( d \)[/tex] and [tex]\( q \)[/tex].
Step 1: Solve the first equation for one variable, say [tex]\( q \)[/tex].
[tex]\[
q = 11 - d
\][/tex]
Step 2: Substitute [tex]\( q = 11 - d \)[/tex] into the total value equation.
[tex]\[
0.10d + 0.25(11 - d) = 1.70
\][/tex]
Step 3: Simplify and solve for [tex]\( d \)[/tex].
[tex]\[
0.10d + 2.75 - 0.25d = 1.70
\][/tex]
Combine like terms:
[tex]\[
-0.15d + 2.75 = 1.70
\][/tex]
Subtract 2.75 from both sides:
[tex]\[
-0.15d = 1.70 - 2.75
\][/tex]
[tex]\[
-0.15d = -1.05
\][/tex]
Divide both sides by [tex]\(-0.15\)[/tex]:
[tex]\[
d = \frac{-1.05}{-0.15} = 7
\][/tex]
Step 4: Use the value of [tex]\( d \)[/tex] to find [tex]\( q \)[/tex].
[tex]\[
q = 11 - d = 11 - 7 = 4
\][/tex]
Thus, the boy has 7 dimes and 4 quarters.
The correct equation that can be used to solve this problem is:
[tex]\[ 0.10d + 0.25(11 - d) = 1.70 \][/tex]
This corresponds to the first equation option provided.
We need to find out how many dimes and quarters the boy has, given that:
1. He has a total of 11 coins.
2. The total value of these coins is [tex]$1.70.
We can define:
- \( d \): the number of dimes.
- \( q \): the number of quarters.
From the information given, we can set up two equations:
1. The total number of coins equation:
\( d + q = 11 \)
2. The total value equation in dollars (remember, a dime is worth $[/tex]0.10 and a quarter is worth $0.25):
[tex]\( 0.10d + 0.25q = 1.70 \)[/tex]
Now, let's use these equations to solve for [tex]\( d \)[/tex] and [tex]\( q \)[/tex].
Step 1: Solve the first equation for one variable, say [tex]\( q \)[/tex].
[tex]\[
q = 11 - d
\][/tex]
Step 2: Substitute [tex]\( q = 11 - d \)[/tex] into the total value equation.
[tex]\[
0.10d + 0.25(11 - d) = 1.70
\][/tex]
Step 3: Simplify and solve for [tex]\( d \)[/tex].
[tex]\[
0.10d + 2.75 - 0.25d = 1.70
\][/tex]
Combine like terms:
[tex]\[
-0.15d + 2.75 = 1.70
\][/tex]
Subtract 2.75 from both sides:
[tex]\[
-0.15d = 1.70 - 2.75
\][/tex]
[tex]\[
-0.15d = -1.05
\][/tex]
Divide both sides by [tex]\(-0.15\)[/tex]:
[tex]\[
d = \frac{-1.05}{-0.15} = 7
\][/tex]
Step 4: Use the value of [tex]\( d \)[/tex] to find [tex]\( q \)[/tex].
[tex]\[
q = 11 - d = 11 - 7 = 4
\][/tex]
Thus, the boy has 7 dimes and 4 quarters.
The correct equation that can be used to solve this problem is:
[tex]\[ 0.10d + 0.25(11 - d) = 1.70 \][/tex]
This corresponds to the first equation option provided.
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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Rewritten by : Jeany
