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 the 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

$\textbf {Hey there, here is the solution.}$

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STEP 1: Define x and y:

Let the number of boys be x

and the number of girls be y

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STEP 2: Form equations:

x + y = 5000

005x + 0.03y = 202

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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

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STEP 4: Find the number of boys and girls:

Boys = x = 2600

Girls = y = 2400

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Answer: There were 2600 boys and 2400 girls last year.

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⭐$\textbf {Cheers}$⭐

Answer 2

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

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

Answer: There were 2600 boys and 2400 girls last year.

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