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Math  /  Algebra

Question4. Brody runs a farm stand that sells surwitwrits and grapes. Each pound of strawberries sells for $2.50\$ 2.50 and each pound of grapes sells for $2\$ 2. Wrody made $160\$ 160 from selling a total of 72 pounds of strawberries and grapes. Find how maty prownds of strawberries and grapes were sol

Studdy Solution

STEP 1

1. Brody sells strawberries and grapes at his farm stand.
2. Each pound of strawberries sells for \$2.50.
3. Each pound of grapes sells for \$2.00.
4. Brody made a total of \$160 from selling strawberries and grapes.
5. Brody sold a total of 72 pounds of strawberries and grapes combined.
6. We need to find how many pounds of strawberries and grapes were sold.

STEP 2

1. Define variables for the number of pounds of strawberries and grapes.
2. Set up a system of equations based on the given information.
3. Solve the system of equations to find the number of pounds of strawberries and grapes sold.

STEP 3

Define variables for the number of pounds of strawberries and grapes.
Let s s be the number of pounds of strawberries sold. Let g g be the number of pounds of grapes sold.

STEP 4

Set up a system of equations based on the given information.
From the total weight sold: s+g=72 s + g = 72
From the total revenue: 2.50s+2g=160 2.50s + 2g = 160

STEP 5

Solve the system of equations to find the number of pounds of strawberries and grapes sold.
First, solve the first equation for one of the variables. Let's solve for g g : g=72−s g = 72 - s
Substitute g=72−s g = 72 - s into the second equation: 2.50s+2(72−s)=160 2.50s + 2(72 - s) = 160
Simplify and solve for s s : 2.50s+144−2s=160 2.50s + 144 - 2s = 160 0.50s+144=160 0.50s + 144 = 160 0.50s=160−144 0.50s = 160 - 144 0.50s=16 0.50s = 16
Divide both sides by 0.50: s=160.50 s = \frac{16}{0.50} s=32 s = 32
Now substitute s=32 s = 32 back into the equation for g g : g=72−32 g = 72 - 32 g=40 g = 40
Brody sold 32 \boxed{32} pounds of strawberries and 40 \boxed{40} pounds of grapes.

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