Trevor tutors french for $12 an hour and scoops ice cream for $8 an hour. he is going to work 20 hours this week. at least how many hours does he need to tutor to make more than $190? let x equal the number of hours he tutors and y be the number of hours he scoops ice cream. at least how many hours does trevor need to tutor to make more than $190? express your answer as a decimal number.
Hours He will work in this Week=20 hours.
Number of Hours he will Teach=x
Number of Hours He will Eat icecream=y
x=20-y (Equation 1)
Let He Total Money he Earn from Teaching.
=12×Number of Hours he work
Total money spent=$8y
But Total Money=$190
We know x+y=20
MEANS He have to teach At least =7.5 hours.To make $190
He needs to tutor x > 7.5
Create two inequalities to represent this situation: one the total number of hours and the other the total amount of money.
Since Trevor works 20 hours or less the inequality must be .
Since Trevor receives $12 each x hour he tutors and $8 per y hour he scoops ice cream, the second inequality is his income for the week which must exceed 190. So write 12x+8y > 190.
Graph the two inequalities to see where they intersect and overlap. See the graph attached.
Let M = total amount of money earned
M = 12x+8y
To make more than $190, the equation is:
Since Trevor is going to scoop ice cream for 20 hours, the equation is:
190<12x+8(20), which simplifies to 190<12x+160.
Isolate x to find the amount of hours that Trevor needs to tutor.
Trevor must tutor for more than 2.5 hours to make more than $190.
the answer is 16 hours
i just multiplied 12(the amount he gets from tutoring) and multiplied it by different numbers to see which one gets him past $190
x > 2.5 hrs
12x + 8(20)= 190
12x + 160 = 190
12x = 30
x > 2.5 hrs