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