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san4es73 [151]
3 years ago
13

There were 180 students in attendance at the dance. If there were 32 more boys than girls at the dance, how many girls and boys

were at the dance?
Mathematics
1 answer:
babymother [125]3 years ago
8 0

\huge\boxed{\text{$74$ girls}}\ \huge\boxed{\text{$106$ boys}}

Hey there! This situation can be modeled and solved using a system of equations. We'll use b to represent the number of boys and g to represent the number of girls.

\displaystyle{\left \{ {{b+g&=180} \atop {b&=g+32} \right.}

Since we know what b equals, we can substitute it into the first equation.

\begin{aligned}b+g&=180\\(g+32)+g&=180&&\smash{\Big|}&&\text{Substitute.}\\2g+32&=180&&\smash{\Big|}&&\text{Combine like terms.}\\2g&=148&&\smash{\Big|}&&\text{Subtract $32$ from both sides.}\\g&=74&&\smash{\Big|}&&\text{Divide both sides by $2$.}\end{aligned}

Now that we know the number of girls, use the second equation to get the number of boys.

\begin{aligned}b&=g+32\\&=74+32&&\smash{\Big|}&&\text{Substitute.}\\&=106&&\smash{\Big|}&&\text{Add.}\end{aligned}

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Answer:

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Large gift: $7

Step-by-step explanation:

Let x represent cost of wrapping each small gift and y represent cost of wrapping each large gift.

We have been given that day one 41 small gifts were wrapped and 45 large were wrapped equaling $397.

We can represent this information in an equation as:

41x+45y=397...(1)

We are also told that day two 30 small gifts were wrapped and 47 large were wrapped equaling $389. We can represent this information in an equation as:

30x+47y=389...(2)  

From equation (1), we will get:

x=\frac{397-45y}{41}

Upon substituting this value in equation (2), we will get:

30(\frac{397-45y}{41})+47y=389

\frac{11910-1350y}{41}+\frac{47*41y}{41}=389

\frac{11910-1350y+1927y}{41}=389

\frac{11910+577y}{41}=389

\frac{11910+577y}{41}\cdot 41=389\cdot 41

11910+577y=15949

11910-11910+577y=15949-11910

577y=4039

\frac{577y}{577}=\frac{4039}{577}

y=7

Therefore, cost to wrap a large gift is $7.

Upon substituting y=7 in equation x=\frac{397-45y}{41}, we will get:

x=\frac{397-45(7)}{41}

x=\frac{397-315}{41}

x=\frac{82}{41}

x=2

Therefore, cost to wrap a small gift is $2.

8 0
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Answer:

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Step-by-step explanation:

According to G0ogle 5 percent equals 1/20 in lowest terms.

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Step-by-step explanation:

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