Question

Write and solve a system of equations: Vanessa and Geneva worked together to buy a pair of tickets ($240 total) to the Green Day Concert. Vanessa earns $10/hr babysitting and Geneva earns $12/hr babysitting. Together they worked 21 hours. How many hours did they each work to earn exactly $240?

Answer 1

The systems of equation are
`\left \{ {{v+g=21} \atop {10v+12g=240}} \right.`.

Vanessa worked for 6 hrs and Geneva worked for 15 hrs to earn exactly $240.

Explanation:

Let the number of hours worked by Vanessa be 'v'.

Let the number of hours worked by Geneva be 'g'.

Given:

Total number of hours worked = 21 hours

So we can say that;

Total number of hours worked is equal to sum of number of hours worked by Vanessa and number of hours worked by Geneva.

framing in equation form we get;

`v+g=21` ⇒ equation 1

Also given:

per hour earnings of Vanessa = $10

per hour earning of Geneva = $12

Total they need to earn = $240

So we can say that;

Total they need to earn would be equal to sum of per hour earnings of Vanessa multiplied by number of hours worked by Vanessa and per hour earning of Geneva multiplied by number of hours worked by Geneva.

framing in equation form we get;

`10v+12g =240` ⇒ equation 2

Hence The systems of equation are
`\left \{ {{v+g=21} \atop {10v+12g=240}} \right.`.

On Solving above equations we get;

First we will multiply equation 1 by 10 we get;

`10(v+g)=21*10`

`10v+10g =210` ⇒ equation 3

Now Subtracting equation 3 from equation 2 we get;

`10v+12g -(10v+10g)=240-210\\\\10v+12g-10v-10g=30\\\\2g =15`

Dividing both side by 2 we get;

`(2g)/(2)=(30)/(2)\\\\g =15\ hrs`

Now Substituting the value of g in equation 1 we get;

`v+g=21\\\\v+15=21\\\\v=21-15 =6\ hrs`

Hence Vanessa worked for 6 hrs and Geneva worked for 15 hrs to earn exactly $240.