Math / Algebra

QuestionWei has $\$ 150.00$ to make a garland using 60 -cent balloons. He wants to purchase 100 blue balloons and some number of white balloons. He learns that the white balloons are on sale for half price. He writes and solves an equation to find the number of white balloons he can purchase. Which models can be used to solve the problem? $100 b+w=150 ; 6,000+w=150$ $100 b+w=150 ; 100 b+30=150$ $0.60 b+0.30 w=150 ; 60+0.30 w=150$ $0.60 b+0.30 w=150 ; 100+0.30 w=150$

Studdy Solution

STEP 1

What is this asking? How many half-price white balloons can Wei buy with $\$150$ if he also buys 100 full-price blue balloons? Watch out! Don't forget to convert cents to dollars and to account for the sale on white balloons!

STEP 2

1. Set up the cost equation
2. Substitute known values
3. Solve for the number of white balloons

STEP 3

Let $b$ be the number of blue balloons and $w$ be the number of white balloons.

STEP 4

The cost of blue balloons is $0.60 \cdot b$ dollars.
Remember, 60 cents is $\$0.60$ .

STEP 5

White balloons are half-price, so they cost $\frac{0.60}{2} = 0.30$ dollars each.
The total cost of white balloons is $0.30 \cdot w$ dollars.

STEP 6

The total cost is the sum of the cost of blue balloons and the cost of white balloons, which must equal Wei's budget of $\$150$ .
So, the equation is $0.60 \cdot b + 0.30 \cdot w = 150$ .

STEP 7

We know Wei wants to buy 100 blue balloons, so $b = 100$ .
Substituting this into our equation gives us $0.60 \cdot 100 + 0.30 \cdot w = 150$ .

STEP 8

Calculating $0.60 \cdot 100$ gives us $60$ .
So, the equation becomes $60 + 0.30 \cdot w = 150$ .

STEP 9

To isolate the term with $w$ , we subtract 60 from both sides of the equation: $60 + 0.30 \cdot w - 60 = 150 - 60$ , which simplifies to $0.30 \cdot w = 90$ .

STEP 10

To solve for $w$ , we divide both sides of the equation by $0.30$ : $\frac{0.30 \cdot w}{0.30} = \frac{90}{0.30}$ .
This gives us $w = 300$ .

STEP 11

Wei can buy 300 white balloons.
The correct model is $0.60b + 0.30w = 150$ and $60 + 0.30w = 150$ .

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Studdy Solution

STEP 1

What is this asking? How many half-price white balloons can Wei buy with $\$150$ if he also buys 100 full-price blue balloons? Watch out! Don't forget to convert cents to dollars and to account for the sale on white balloons!

STEP 2

1. Set up the cost equation
2. Substitute known values
3. Solve for the number of white balloons

STEP 3

Let $b$ be the number of blue balloons and $w$ be the number of white balloons.

STEP 4

The cost of blue balloons is $0.60 \cdot b$ dollars.
Remember, 60 cents is $\$0.60$ .

STEP 5

White balloons are half-price, so they cost $\frac{0.60}{2} = 0.30$ dollars each.
The total cost of white balloons is $0.30 \cdot w$ dollars.

STEP 6

The total cost is the sum of the cost of blue balloons and the cost of white balloons, which must equal Wei's budget of $\$150$ .
So, the equation is $0.60 \cdot b + 0.30 \cdot w = 150$ .

STEP 7

We know Wei wants to buy 100 blue balloons, so $b = 100$ .
Substituting this into our equation gives us $0.60 \cdot 100 + 0.30 \cdot w = 150$ .

STEP 8

Calculating $0.60 \cdot 100$ gives us $60$ .
So, the equation becomes $60 + 0.30 \cdot w = 150$ .

STEP 9

To isolate the term with $w$ , we subtract 60 from both sides of the equation: $60 + 0.30 \cdot w - 60 = 150 - 60$ , which simplifies to $0.30 \cdot w = 90$ .

STEP 10

To solve for $w$ , we divide both sides of the equation by $0.30$ : $\frac{0.30 \cdot w}{0.30} = \frac{90}{0.30}$ .
This gives us $w = 300$ .

STEP 11

Wei can buy 300 white balloons.
The correct model is $0.60b + 0.30w = 150$ and $60 + 0.30w = 150$ .

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Studdy Solution

STEP 1

What is this asking? How many half-price white balloons can Wei buy with $150\$150$150 if he also buys 100 full-price blue balloons? Watch out! Don't forget to convert cents to dollars and to account for the sale on white balloons!

STEP 2

1. Set up the cost equation2. Substitute known values3. Solve for the number of white balloons

STEP 3

Let bbb be the number of blue balloons and www be the number of white balloons.

STEP 4

The cost of blue balloons is 0.60⋅b0.60 \cdot b0.60⋅b dollars.Remember, 60 cents is $0.60\$0.60$0.60.

STEP 5

White balloons are half-price, so they cost 0.602=0.30\frac{0.60}{2} = 0.3020.60​=0.30 dollars each.The total cost of white balloons is 0.30⋅w0.30 \cdot w0.30⋅w dollars.

STEP 6

The total cost is the sum of the cost of blue balloons and the cost of white balloons, which must equal Wei's budget of $150\$150$150.So, the equation is 0.60⋅b+0.30⋅w=1500.60 \cdot b + 0.30 \cdot w = 1500.60⋅b+0.30⋅w=150.

STEP 7

We know Wei wants to buy 100 blue balloons, so b=100b = 100b=100.Substituting this into our equation gives us 0.60⋅100+0.30⋅w=1500.60 \cdot 100 + 0.30 \cdot w = 1500.60⋅100+0.30⋅w=150.

STEP 8

Calculating 0.60⋅1000.60 \cdot 1000.60⋅100 gives us 606060.So, the equation becomes 60+0.30⋅w=15060 + 0.30 \cdot w = 15060+0.30⋅w=150.

STEP 9

To isolate the term with www, we subtract 60 from both sides of the equation: 60+0.30⋅w−60=150−6060 + 0.30 \cdot w - 60 = 150 - 6060+0.30⋅w−60=150−60, which simplifies to 0.30⋅w=900.30 \cdot w = 900.30⋅w=90.

STEP 10

To solve for www, we divide both sides of the equation by 0.300.300.30: 0.30⋅w0.30=900.30\frac{0.30 \cdot w}{0.30} = \frac{90}{0.30}0.300.30⋅w​=0.3090​.This gives us w=300w = 300w=300.

STEP 11

Wei can buy **300** white balloons.The correct model is 0.60b+0.30w=1500.60b + 0.30w = 1500.60b+0.30w=150 and 60+0.30w=15060 + 0.30w = 15060+0.30w=150.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? How many half-price white balloons can Wei buy with $\$150$ if he also buys 100 full-price blue balloons? Watch out! Don't forget to convert cents to dollars and to account for the sale on white balloons!

1. Set up the cost equation
2. Substitute known values
3. Solve for the number of white balloons

Let $b$ be the number of blue balloons and $w$ be the number of white balloons.

The cost of blue balloons is $0.60 \cdot b$ dollars.
Remember, 60 cents is $\$0.60$ .

White balloons are half-price, so they cost $\frac{0.60}{2} = 0.30$ dollars each.
The total cost of white balloons is $0.30 \cdot w$ dollars.

The total cost is the sum of the cost of blue balloons and the cost of white balloons, which must equal Wei's budget of $\$150$ .
So, the equation is $0.60 \cdot b + 0.30 \cdot w = 150$ .

We know Wei wants to buy 100 blue balloons, so $b = 100$ .
Substituting this into our equation gives us $0.60 \cdot 100 + 0.30 \cdot w = 150$ .

Calculating $0.60 \cdot 100$ gives us $60$ .
So, the equation becomes $60 + 0.30 \cdot w = 150$ .

To isolate the term with $w$ , we subtract 60 from both sides of the equation: $60 + 0.30 \cdot w - 60 = 150 - 60$ , which simplifies to $0.30 \cdot w = 90$ .

To solve for $w$ , we divide both sides of the equation by $0.30$ : $\frac{0.30 \cdot w}{0.30} = \frac{90}{0.30}$ .
This gives us $w = 300$ .

Wei can buy 300 white balloons.
The correct model is $0.60b + 0.30w = 150$ and $60 + 0.30w = 150$ .