Question

1. a daycare has a child - to - caregiver ratio of 3:1. the total number of children and caregivers was 32 last year and 48 this year. how many children and caregivers were there for each of these two years? a. last year: 24 caregivers, 8 children. this year: 36 caregivers, 12 children. b. last year: 8 caregivers, 24 children. this year: 12 caregivers, 36 children. c. last year: 12 caregivers, 20 children. this year: 16 caregivers, 32 children. d. last year: 10 caregivers, 22 children. this year: 14 caregivers, 34 children.

Explanation:

Step1: Define ratio parts

The child-to-caregiver ratio is $3:1$, so total parts = $3+1=4$.

Step2: Calculate last year counts

Total people last year = 32.
Caregivers: $\frac{1}{4} \times 32 = 8$
Children: $\frac{3}{4} \times 32 = 24$

Step3: Calculate this year counts

Total people this year = 48.
Caregivers: $\frac{1}{4} \times 48 = 12$
Children: $\frac{3}{4} \times 48 = 36$

Answer:

b. Last year: 8 caregivers, 24 children.
This year: 12 caregivers, 36 children.