Yesterday, a movie theater sold 279 bags of popcorn. A large bag of popcorn costs $4. A small bag of popcorn costs $1. In all, the movie theater made $567 from popcorn sales. Write and solve a system of equations to find how many bags of each size of popcorn were sold.

two equations, 1)S+L=279, 2)1S+4L=567

96 Larges, 183 Smalls

Step-by-step explanation:

Solve for L:

multiply the first one by -1,

-S-L=-279

Subtract:

-S-L=-279

- S+4L=567

3L=288

Divide 288 by 3:

288/3=96

96=L, 96 larges

Solve for S:

We only need to use one equation since we already have L:

S+(96)=279

Take down parenthesis since no distribution

Subtract 96 from both sides:

S=183

Check:

183+96=279

183(1)+96(4)=567

183+384=567

567=567

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yes because they have the same amount of green and blur marbles.

step-by-step explanation:

proportions are fractions that equal to each other. so if two fractions are the same, they are proportional.

let's check the answers to see if they are proportional.

question a is not proportional because you can't turn 1.5/3 to 3/9. if you try to multiply 1.5/3 by 2 or 3, you wont get 3/9. it's impossible to make the fractions the same.

question b is not proportional because you can't turn 22/33 to 4/6. 33 can't go into 6.

question c is proportional because when you multiply 2 and 3 by 71, you would get 142/213, and those fractions equal to each other

question d is proportional because when you divide 14 and 7 by 2, you would end up with 7/3.5, and those fractions equal to each other.