Math / Algebra

QuestionTerrell arranges $x$ roses at $\$ 3.50$ each with 10 carnations at $\$ 2.25$ each. He makes a bouquet of flowers that averages $\$ 3.00$ per flower. Select the equation that models the situation. A. $3.50 x+2.25(10)=3(x+10)$ B. $3.50 x+2.25=0.75 x$ C. $3.50 x+3=22.5(x+10)$ D. $3.50 x+2.50=0.75(x+10)$

Studdy Solution

STEP 1

What is this asking? How many $\$3.50$ roses do we need to mix with ten $\$2.25$ carnations to get a bouquet with an average cost of $\$3.00$ per flower? Watch out! Don't forget that the average cost is the total cost divided by the total number of flowers!

STEP 2

1. Set up the equation
2. Solve for x

STEP 3

The cost of the roses is the price per rose times the number of roses, which is $\$3.50 \cdot x = \$3.50x$ .

STEP 4

The cost of the carnations is the price per carnation times the number of carnations, which is $\$2.25 \cdot 10 = \$22.50$ .

STEP 5

The total cost of the bouquet is the cost of the roses plus the cost of the carnations: $\$3.50x + \$22.50$ .

STEP 6

The total number of flowers in the bouquet is the number of roses plus the number of carnations: $x + 10$ .

STEP 7

The average cost per flower is the total cost divided by the total number of flowers.
We're told this is $\$3.00$ , so $\frac{\$3.50x + \$22.50}{x + 10} = \$3.00$ .

STEP 8

Multiply both sides of our equation by $x + 10$ to get $\$3.50x + \$22.50 = \$3.00(x + 10)$ .
Look closely, and we see this matches option A!

STEP 9

Distribute the 3 on the right side of the equation: $3.50x + 22.50 = 3x + 30$ .
Remember, we're doing this to simplify the right side of the equation.

STEP 10

Subtract $3x$ from both sides of the equation: $0.50x + 22.50 = 30$ .
We're subtracting $3x$ to move all the terms with $x$ to one side of the equation.

STEP 11

Subtract $22.50$ from both sides: $0.50x = 7.50$ .
We're subtracting $22.50$ to get the term with $x$ by itself.

STEP 12

Divide both sides by $0.50$ : $x = 15$ .
Dividing by $0.50$ isolates $x$ and gives us our answer!

STEP 13

The equation that models the situation is A.
Terrell used 15 roses.

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Studdy Solution

STEP 1

What is this asking? How many $\$3.50$ roses do we need to mix with ten $\$2.25$ carnations to get a bouquet with an average cost of $\$3.00$ per flower? Watch out! Don't forget that the average cost is the total cost divided by the total number of flowers!

STEP 2

1. Set up the equation
2. Solve for x

STEP 3

The cost of the roses is the price per rose times the number of roses, which is $\$3.50 \cdot x = \$3.50x$ .

STEP 4

The cost of the carnations is the price per carnation times the number of carnations, which is $\$2.25 \cdot 10 = \$22.50$ .

STEP 5

The total cost of the bouquet is the cost of the roses plus the cost of the carnations: $\$3.50x + \$22.50$ .

STEP 6

The total number of flowers in the bouquet is the number of roses plus the number of carnations: $x + 10$ .

STEP 7

The average cost per flower is the total cost divided by the total number of flowers.
We're told this is $\$3.00$ , so $\frac{\$3.50x + \$22.50}{x + 10} = \$3.00$ .

STEP 8

Multiply both sides of our equation by $x + 10$ to get $\$3.50x + \$22.50 = \$3.00(x + 10)$ .
Look closely, and we see this matches option A!

STEP 9

Distribute the 3 on the right side of the equation: $3.50x + 22.50 = 3x + 30$ .
Remember, we're doing this to simplify the right side of the equation.

STEP 10

Subtract $3x$ from both sides of the equation: $0.50x + 22.50 = 30$ .
We're subtracting $3x$ to move all the terms with $x$ to one side of the equation.

STEP 11

Subtract $22.50$ from both sides: $0.50x = 7.50$ .
We're subtracting $22.50$ to get the term with $x$ by itself.

STEP 12

Divide both sides by $0.50$ : $x = 15$ .
Dividing by $0.50$ isolates $x$ and gives us our answer!

STEP 13

The equation that models the situation is A.
Terrell used 15 roses.

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Studdy Solution

STEP 1

What is this asking? How many $3.50\$3.50$3.50 roses do we need to mix with ten $2.25\$2.25$2.25 carnations to get a bouquet with an average cost of $3.00\$3.00$3.00 per flower? Watch out! Don't forget that the average cost is the *total cost* divided by the *total number* of flowers!

STEP 2

1. Set up the equation2. Solve for *x*

STEP 3

The cost of the roses is the price per rose times the number of roses, which is $3.50⋅x=$3.50x \$3.50 \cdot x = \$3.50x $3.50⋅x=$3.50x.

STEP 4

The cost of the carnations is the price per carnation times the number of carnations, which is $2.25⋅10=$22.50 \$2.25 \cdot 10 = \$22.50 $2.25⋅10=$22.50.

STEP 5

The total cost of the bouquet is the cost of the roses *plus* the cost of the carnations: $3.50x+$22.50 \$3.50x + \$22.50 $3.50x+$22.50.

STEP 6

The total number of flowers in the bouquet is the number of roses *plus* the number of carnations: x+10 x + 10 x+10.

STEP 7

The average cost per flower is the *total cost* divided by the *total number* of flowers.We're told this is $3.00\$3.00$3.00, so $3.50x+$22.50x+10=$3.00 \frac{\$3.50x + \$22.50}{x + 10} = \$3.00 x+10$3.50x+$22.50​=$3.00.

STEP 8

Multiply both sides of our equation by x+10x + 10x+10 to get $3.50x+$22.50=$3.00(x+10) \$3.50x + \$22.50 = \$3.00(x + 10) $3.50x+$22.50=$3.00(x+10).Look closely, and we see this matches option A!

STEP 9

Distribute the 3 on the right side of the equation: 3.50x+22.50=3x+30 3.50x + 22.50 = 3x + 30 3.50x+22.50=3x+30.Remember, we're doing this to simplify the right side of the equation.

STEP 10

Subtract 3x3x3x from both sides of the equation: 0.50x+22.50=30 0.50x + 22.50 = 30 0.50x+22.50=30.We're subtracting 3x3x3x to move all the terms with xxx to one side of the equation.

STEP 11

Subtract 22.5022.5022.50 from both sides: 0.50x=7.50 0.50x = 7.50 0.50x=7.50.We're subtracting 22.5022.5022.50 to get the term with xxx by itself.

STEP 12

Divide both sides by 0.500.500.50: x=15 x = 15 x=15.Dividing by 0.500.500.50 isolates xxx and gives us our answer!

STEP 13

The equation that models the situation is **A**.Terrell used **15** roses.

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What is this asking? How many $\$3.50$ roses do we need to mix with ten $\$2.25$ carnations to get a bouquet with an average cost of $\$3.00$ per flower? Watch out! Don't forget that the average cost is the total cost divided by the total number of flowers!

1. Set up the equation
2. Solve for x

The cost of the roses is the price per rose times the number of roses, which is $\$3.50 \cdot x = \$3.50x$ .

The cost of the carnations is the price per carnation times the number of carnations, which is $\$2.25 \cdot 10 = \$22.50$ .

The total cost of the bouquet is the cost of the roses plus the cost of the carnations: $\$3.50x + \$22.50$ .

The total number of flowers in the bouquet is the number of roses plus the number of carnations: $x + 10$ .

The average cost per flower is the total cost divided by the total number of flowers.
We're told this is $\$3.00$ , so $\frac{\$3.50x + \$22.50}{x + 10} = \$3.00$ .

Multiply both sides of our equation by $x + 10$ to get $\$3.50x + \$22.50 = \$3.00(x + 10)$ .
Look closely, and we see this matches option A!

Distribute the 3 on the right side of the equation: $3.50x + 22.50 = 3x + 30$ .
Remember, we're doing this to simplify the right side of the equation.

Subtract $3x$ from both sides of the equation: $0.50x + 22.50 = 30$ .
We're subtracting $3x$ to move all the terms with $x$ to one side of the equation.

Subtract $22.50$ from both sides: $0.50x = 7.50$ .
We're subtracting $22.50$ to get the term with $x$ by itself.

Divide both sides by $0.50$ : $x = 15$ .
Dividing by $0.50$ isolates $x$ and gives us our answer!

The equation that models the situation is A.
Terrell used 15 roses.