Question

2) CCBC is planning to purchase a total of $500 blue and gold balloons to decorate for graduation. They want

three times as many blue balloons as gold balloons. How many of each should they buy?
Find/Unknown:
Equation:
Solve:
Solution/Interpretation:

Answer 1

Find/Unknown:

The number of blue balloons (B) and the number of gold balloons (G) that CCBC should buy.

Equation:

B + G = 500 (the total number of balloons should be 500)

B = 3G (they want three times as many blue balloons as gold balloons)

Solve:

To solve this system of equations, we can use the second equation to express B in terms of G (B = 3G) and then substitute this expression into the first equation.

Substitute B = 3G into equation 1:

3G + G = 500

Combine like terms:

4G = 500

Now, solve for G by dividing both sides by 4:

G = 500 / 4

G = 125

Now that we know the number of gold balloons (G), we can find the number of blue balloons (B) using B = 3G:

B = 3 * 125

B = 375

So, CCBC should buy 375 blue balloons and 125 gold balloons to decorate for graduation.

Solution/Interpretation:

CCBC should buy 375 blue balloons and 125 gold balloons to meet their decoration requirements. This arrangement satisfies the condition of having three times as many blue balloons as gold balloons and a total of 500 balloons.

Explanation:

Answer 2

Blue balloons = 375

Gold balloons = 125

Explanation:

Find/Unknown:

• The number of blue balloons
• The number of gold balloons

Equation:

Let x be the number of gold balloons.

The number of blue balloons is 3x.

The total cost of the blue and gold balloons is 500.

x + 3x = 500

Solve:

Combining like terms, we get:

4x = 500

Dividing both sides by 4, we get:

`\sf (4x )/(4)=( 500)/(4)`

x = 125

Therefore, the number of gold balloons is 125.

The number of blue balloons is 3 × 125 = 375.

Solution/Interpretation:

CCBC should buy 375 blue balloons and 125 gold balloons.