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

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 Quiz Active 1 2 3 4 5 6 $\square$ 8 3 10 time remanning 56:22 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 Mark this and return Save and Exit Next Submit
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Solution

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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}\\).

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