Question

Last year the total number of students in a
school was 5000. This year, the number of
boys increased by 5% and that of girls by
3% and the total number of students
increased by 202. How many boys and girls
were there in the school last year?​

Answer 1

Answer:

last year total number of students in a school was 5000.

b + g = 5000

g = -b + 5000

this year the number of boys increased by 5% and that of girls increased by 3%.

the total number of students increased by 202 to.

.05b + .03g = 202

how many boys and girls were there in a school last year.

Replace g = -b+5000

.05b + .03(-b+5000) = 202

.05b - .03b + 150 = 202

.02b = 202 - 150

.02b = 52

b = 52/.02

b = 2600 boys

and

b = 5000 - 2600

b = 2400 girls

:

:

Check

.05(2600) = 130

.03(2400) = 72

-------------------

total increase: 202

:

Answer 2

Answer:

There were 2600 boys and 2400 girls last year.

Step-by-step explanation:

STEP 1: Define x and y:

Let the number of boys be x

and the number of girls be y

.............................................................................................

STEP 2: Form equations:

x + y = 5000

005x + 0.03y = 202

.............................................................................................

STEP 3: Solve x and y:

x + y = 5000 ---------------------------------- [ 1 ]

0.05x + 0.03y = 202 --------------------- [ 2 ]

.

From [ 1 ]:

x + y = 5000

x = 5000 - y --------------------- Sub into [ 2 ]

.

0.05x + 0.03y = 202

0.05 ( 5000 - y) + 0.03y = 202

250 - 0.05y + 0.03y = 202

0.02y = 48

y = 2400 -------------------- Sub into [ 1 ]

.

x + y = 5000

x + 2400 = 5000

x = 2600

STEP 4: Find the number of boys and girls:

Boys = x = 2600

Girls = y = 2400

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