Depth · one concept from first principles · step 2 of 4
At a bazaar snack corner, a cup of coffee costs won and a slice of cake costs won, and anyone who buys both at once gets off the combined price. On the first day, people bought something at the snack corner, and total sales were won. people bought coffee, and no one bought more than one of the same item. How many people bought cake?
Everyone bought something, so the buyers who did not buy coffee bought only cake.
In the Venn diagram, the part of the cake circle outside the coffee circle is fixed at once.
7.EE.B.3Draw A Venn DiagramCoffee and cake together cost 220 won, less 10%.
A 10% discount leaves 90% of the price.
7.RP.A.3Identify SubproblemsLet x people buy both. Then 86 - x bought coffee only.
Each group pays its own price, and the three groups together make the day's sales.
7.EE.B.4Convert To AlgebraIf people bought both, the day's sales are won.
Every buyer is in exactly one group, coffee only, cake only, or both, so the three groups' sales add up to the total.
Coffee-only buyers number , and the people without coffee bought cake only.
The coffee buyers split into those who also took cake and those who did not, with no one in both, so the two counts add to .
Taking the combo buyers back out of leaves .
Each group brings in its headcount times its price, and a combo costs won.
people each paying won is equal groups of won.
Ten percent off leaves out of every won, so becomes .
Expand and collect the x terms.
Each combo buyer brings in 78 won more than a coffee-only buyer.
7.EE.B.4Convert To AlgebraCake buyers are the cake-only group plus the both group.
Read the whole cake circle off the diagram.
7.EE.B.3Draw A Venn DiagramSort people into non-overlapping groups first, and one unknown is often enough.
A parent dashboard for the family lives at sensimlab.com.