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Answer :
To determine how many additional candy bars James still needs to sell, we need to set up and solve an inequality.
1. Identify Known Values:
- Each candy bar costs [tex]$3.
- James' parents already bought candy worth $[/tex]21.
- James needs to sell at least [tex]$150 worth of candy to earn prizes.
2. Set up the Inequality:
- Let \( c \) represent the number of additional candy bars James needs to sell.
- The value of the candy bars that James needs to sell, plus the $[/tex]21 worth of candy bars already bought, should be at least $150.
- This can be written as:
[tex]\[
3c + 21 \geq 150
\][/tex]
3. Solve the Inequality:
- First, subtract 21 from both sides:
[tex]\[
3c \geq 150 - 21
\][/tex]
- Simplify the right side:
[tex]\[
3c \geq 129
\][/tex]
- Divide both sides by 3 to find the value of [tex]\( c \)[/tex]:
[tex]\[
c \geq \frac{129}{3}
\][/tex]
- Calculate the division:
[tex]\[
c \geq 43
\][/tex]
Therefore, James needs to sell at least 43 additional candy bars to earn the prizes. The correct inequality that shows how many candy bars James still needs to sell is:
[tex]\[
3c + 21 \geq 150
\][/tex]
1. Identify Known Values:
- Each candy bar costs [tex]$3.
- James' parents already bought candy worth $[/tex]21.
- James needs to sell at least [tex]$150 worth of candy to earn prizes.
2. Set up the Inequality:
- Let \( c \) represent the number of additional candy bars James needs to sell.
- The value of the candy bars that James needs to sell, plus the $[/tex]21 worth of candy bars already bought, should be at least $150.
- This can be written as:
[tex]\[
3c + 21 \geq 150
\][/tex]
3. Solve the Inequality:
- First, subtract 21 from both sides:
[tex]\[
3c \geq 150 - 21
\][/tex]
- Simplify the right side:
[tex]\[
3c \geq 129
\][/tex]
- Divide both sides by 3 to find the value of [tex]\( c \)[/tex]:
[tex]\[
c \geq \frac{129}{3}
\][/tex]
- Calculate the division:
[tex]\[
c \geq 43
\][/tex]
Therefore, James needs to sell at least 43 additional candy bars to earn the prizes. The correct inequality that shows how many candy bars James still needs to sell is:
[tex]\[
3c + 21 \geq 150
\][/tex]
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