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Savatey [412]
3 years ago
6

A middle school has a speech club with a total of 18 students. The ratio of girls to boys is 4:5. How many girls are in the spee

ch club? How many boys are in the speech club? Justify your answers. (using linear equations)
Mathematics
1 answer:
Fantom [35]3 years ago
8 0
The ratio is 4:5
so girls=4x
and boys=5x
(because you don't know how many boys or girls there are)
then the equation would be
4x+5x=18
9x=18
so x=2
 then 2 times 4 which equals 8
and 2 times 5 which equals 10

so there are 8 girls and 10 boys

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Sara has $50 in her wallet in $5 and $20 bills. Create a linear equation (with
77julia77 [94]

Answer:

<em>0 $20 bills and 10 $5 bills</em>

<em>1 $20 bills and 6 $5 bills</em>

<em>2 $20 bills and 2 $5 bills</em>

Step-by-step explanation:

<u>Equations</u>

Let's set:

x=number of $5 bills

y=number of $20 bills

The total amount Sara has is given by

5x+20y

And we know it's equal to $50, thus:

5x+20y=50

Dividing by 5

x+4y=10

We would need another condition to solve for x and y, but we can determine some combinations that solve the problem.

Solving for x:

x=10-4y

Since both x and y are integers and cannot be negative:

10-4y≥0

Swapping sides:

4y≤10

Dividing by 4:

y≤2.5

Thus, y can only have the values {0,1,2}

For y=0

x=10-4*0=10

x=10

For y=1

x=10-4*1=6

x=6

For y=2

x=10-4*2=2

x=2

Thus, the possible combinations are:

0 $20 bills and 10 $5 bills

1 $20 bills and 6 $5 bills

2 $20 bills and 2 $5 bills

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