# SAT Math: Which Inequalities Represent a Baker's Dilemma?

Eleanor needs to prepare at least 10 cakes before her restaurant opens in 5 hours. She can bake a red velvet cake in 30 minutes and a chocolate cake in 45 minutes. Because her oven is very small, she can only bake one cake at a time. If a represents the number of red velvet cakes she can make and b represents the number of chocolate cakes she can make, which of the following systems of inequalities best represents Eleanor's situation?

Heart of Algebra | Systems of linear inequalities in two variables (word problems) |

Product Type | SAT Math |

SAT | SAT Math |

SAT Math | Algebra and Functions Heart of Algebra |

Test Prep | SAT Math |

### Transcript

minutes because mother is very small but only one case

at a time If represents red delegates you could make

and be represents a number of chocolate cakes you could

make it a filing system follows Best represent eleanor situation

Okay so we're just kind of noodling over the question

here and note that she could bake on ly red

velvet cakes to an hour and we'll that would actually

get her there because she's got to make ten cakes

in five hours and she's gotta have two an hour

so it looks like she doesn't have any room for

chocolate cakes because they take forty five minutes So there's

gonna be an interesting problem in the restaurant So yeah

eleanor is a bit pressed for time so we're going

to figure out this math conundrum for her while she

preps ingredients It takes eleanor thirty minutes to make a

red velvet cake in forty five minutes to make a

chocolate cake Yes Were musing over this because it adds

a lot of complexity of the problem But she has

only five hours till convert all of this in two

minutes to make the unit's match up Right That's The

first thing you always do in these kind of problems

Get the unit's teo sink sixty minutes per hour times

five hours is three hundred minutes that's all the time

She has so she should spend less than or equal

to three hundred minutes So the questions already given us

what the variables are here A and b the cakes

and it's going to be thirty eight for the red

velvet and forty five for the chocolate thing Right So

thirty eight plus forty five b is got to be

less than or equal to the three hundred there And

they're all minutes Here is what we're referring to Eleanor

needs at least ten plates Have dessert for her restaurant

Meaning the number of red velvet cakes eh And the

number of chocolate cakes be must be greater than or

equal to ten So a plus b has to be

Greater than or equal to ten just like that All

right well the two inequalities that represent eleanor situation are

thirty eight plus forty five is less than three hundred

and a plus b is greater than yours able to

ten So that's the answer there See yeah we hope

eleanor will share some of the leftovers with us for

helping around She must make at least ten cakes so

less than or equal to wouldn't work here So get

rid of that one and she only has five hours

so using greater than or equal to and that equality

would be no good either So being the those guys 00:02:17.888 --> [endTime] okay passed the fourth