Questions: Chen is bringing fruit and veggies to serve at an afternoon meeting. He spends a total of 28.70 on 5 pints of cut veggies and 7 pints of cut fruit. The food cost is modeled by the equation 5v+7f=28.70, where v represents the cost of one pint of cut veggies and f represents the cost of one pint of cut fruit. If the cost of each pint of fruit is 2.85, what is the approximate price of a pint of veggies? (Round to the nearest cent, as needed.)
1.75
2.06
2.39
3.99
Transcript text: Writing and Solving Equations in Two Variables
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Chen is bringing fruit and veggies to serve at an afternoon meeting. He spends a total of $\$ 28.70$ on 5 pints of cut veggies and 7 pints of cut fruit. The food cost is modeled by the equation $5 \mathrm{v}+7 f=28.70$, where $v$ represents the cost of one pint of cut veggies and f represents the cost of one pint of cut fruit. If the cost of each pint of fruit is $\$ 2.85$, what is the approximate price of a pint of veggies? (Round to the nearest cent, as needed.)
\$1.75
\$2.06
\$2.39
\$3.99
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Solution
Solution Steps
To find the approximate price of a pint of veggies, we need to solve the equation \(5v + 7f = 28.70\) for \(v\), given that the cost of each pint of fruit \(f\) is \$2.85. Substitute \(f = 2.85\) into the equation and solve for \(v\).
Step 1: Set Up the Equation
We start with the equation representing the total cost of the fruit and veggies:
\[
5v + 7f = 28.70
\]
where \(v\) is the cost of one pint of cut veggies and \(f\) is the cost of one pint of cut fruit.
Step 2: Substitute the Known Value
We know that the cost of each pint of fruit is \(f = 2.85\). Substituting this value into the equation gives:
\[
5v + 7(2.85) = 28.70
\]
Step 3: Simplify and Solve for \(v\)
Calculating \(7 \times 2.85\):
\[
7 \times 2.85 = 19.95
\]
Now, substituting this back into the equation:
\[
5v + 19.95 = 28.70
\]
Subtracting \(19.95\) from both sides:
\[
5v = 28.70 - 19.95
\]
Calculating the right side:
\[
5v = 8.75
\]
Now, dividing both sides by \(5\):
\[
v = \frac{8.75}{5} = 1.75
\]
Final Answer
The approximate price of a pint of veggies is \\(\boxed{1.75}\\).