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Juliana and Maria logged a total of 90 hours working for their dad. Juliana worked 2 hours more than three times as much as Maria. How many hours did Juliana work?

Respuesta :

Louli
Answer:
Juliana worked 68 hours

Explanation:
Assume the hours logged by Juliana is x
Assume the hours logged by Maria is y

We are given that:
1- Total hours logged by both is 90. This means that:
x + y = 90 
This equation can be rewritten as:
x = 90 - y ...........> equation I

2- Juliana worked 2 hours more than 3 times as much as Maria. This means that:
x = 3y + 2 ...........> equation II

Substitute with equation I in equation II and solve for y as follows:
x = 3y + 2
90 - y = 3y + 2
88 = 4y
y = 22

Substitute with y in equation I to get x as follows:
x = 90 - y
x = 90 - 22
x = 68

Based on the above:
Hours logged by Juliana = x = 68 hours
Hours logged by Maria = y = 22 hours

Hope this helps :)
calculista

Let

x---------> the hours logged by Juliana

y--------->  the hours logged by Maria

we know that

[tex]x+y=90[/tex] ---------> equation [tex]1[/tex]

[tex]x=3y+2[/tex] ---------> equation [tex]2[/tex]

Substitute equation [tex]2[/tex] in equation [tex]1[/tex]

[tex](3y+2)+y=90[/tex]

[tex]4y+2=90[/tex]

[tex]4y=90-2[/tex]

[tex]4y=88[/tex]

[tex]y=88/4[/tex]

[tex]y=22\ hours[/tex]

Find the value of x

[tex]x=3y+2[/tex]

[tex]x=3*22+2[/tex]

[tex]x=68\ hours[/tex]

therefore

the answer is

Juliana worked [tex]68\ hours[/tex]

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