Depth · one concept from first principles · step 2 of 4
The ratio 4:3 means 4x classes of 18 and 3x classes of 19, so 7x classrooms in all.
A ratio becomes actual counts once we multiply both parts by the same x.
6.RP.A.3Identify SubproblemsWith 18 per class, one extra room's worth of children is left over, so there are enough children for 7x + 1 classes of 18.
Being one room short means one more class of 18 than there are rooms.
7.EE.B.4Convert To AlgebraAdd up the 18-child and the 19-child classes.
Same children, counted a second way.
7.EE.B.4Convert To AlgebraBoth expressions count the same children.
The 3x classes of 19 each take one extra child, and together they absorb the 18 left over.
7.EE.B.4Change Focus Count The ComplementCounting the children both ways gives , so .
Both expressions count the same children, so each equals the true number and therefore each other.
One room short with left over means one more class of than there are rooms, .
The second plan has classes of and classes of , which hold children.
A ratio means the two class counts are copies and copies of one same amount .
classes of children is equal groups of .
Taking from both sides leaves , and dividing both sides by gives .
There are 7 × 6 = 42 classrooms.
Use either count; the first one is quickest.
7.EE.B.3Convert To AlgebraWhen two plans place the same children, count them both ways and set the counts equal.
A parent dashboard for the family lives at sensimlab.com.