Question

The school administration decided that four grade levels of students (K–3) will share donated funds according to the proportion of students that are in each grade. There are twice as many students in third grade as there are in second grade. There are 5 more students in first grade than there are in second grade. The number of students in kindergarten is 15 more than in first grade. There are 365 students in the K–3 grades at the school.

(A) How many students are in each grade?

(B) What fraction of the money should each grade get?

Answer 1

There are 90 students in kindergarten, 75 in first grade, 70 in second grade, and 140 in third grade. Kindergarten gets 90/365, first grade gets 75/365, second grade gets 70/365, and third grade gets 140/365 of the funds.

Step-by-step explanation:

A student has asked how many students are in each grade level (K-3) given that there are 365 students in total, with twice as many students in third grade as in second grade, 5 more in first grade than in second, and 15 more in kindergarten than in first. Let's define the number of students in second grade as x. Then, the number of students in third grade is 2x, in first grade is x + 5, and in kindergarten is x + 5 + 15.

Solving the System of Equations

Setting up the equation based on the total number of students we get:

Kindergarten: x + 20

First grade: x + 5

Second grade: x

Third grade: 2x

Adding these together equals the total number of students:

x + (x + 20) + (x + 5) + 2x = 365

Solving for x we find that x = 70, thus:

Kindergarten: 90 students

First grade: 75 students

Second grade: 70 students

Third grade: 140 students

Distributing the Funds

To determine the fraction of the money each grade gets, we divide the number of students by the total:

Kindergarten gets 90/365 of the funds

First grade gets 75/365 of the funds

Second grade gets 70/365 of the funds

Third grade gets 140/365 of the funds