Mat1182640_en 3K + (D ÷ 1/4 + 2M) − (−5)² = ?

 

ENGLISH VERSION

PEMDAS STEP-BY-STEP SOLUTION

Given:  3K + 2K = 75

D × K = 75

M = 5²

Find:  3K + (D ÷ 1/4 + 2M) − (−5)² = ?

PEMDAS means:

P = Parentheses
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction

STEP 1 — Find the value of K

We are given:

3K + 2K = 75

Combine like terms:  5K = 75

Divide both sides by 5:

K = 75 ÷ 5

K = 15

Therefore:  K = 15

STEP 2 — Find the value of D

We are given:  D × K = 75

We already know:  K = 15

Substitute K = 15:  D × 15 = 75

Divide both sides by 15:

D = 75 ÷ 15

D = 5

Therefore:  D = 5

STEP 3 — Find the value of M

We are given:  M = 5²

According to the Exponents rule:

5² = 5 × 5

= 25

Therefore:  M = 25

STEP 4 — Substitute K, D, and M

The original expression is: 3K + (D ÷ 1/4 + 2M) − (−5)²

Substitute:

K = 15
D = 5
M = 25

We get:  3(15) + (5 ÷ 1/4 + 2(25)) − (−5)²

STEP 5 — Exponents

According to PEMDAS, calculate the exponent:  (−5)² = 25

The expression becomes:  3(15) + (5 ÷ 1/4 + 2(25)) − 25

STEP 6 — Division

Calculate:  5 ÷ 1/4

Dividing by 1/4 is the same as multiplying by 4:

5 ÷ 1/4 = 5 × 4 = 20

Now:   3(15) + (20 + 2(25)) − 25

STEP 7 — Multiplication

Calculate the multiplications:

3 × 15 = 45

2 × 25 = 50

So:  45 + (20 + 50) − 25

STEP 8 — Parentheses

Calculate inside the parentheses:  20 + 50 = 70

Now:  45 + 70 − 25

STEP 9 — Addition and Subtraction

Addition and subtraction have the SAME priority.

Therefore, work from LEFT TO RIGHT:

45 + 70 = 115

115 − 25 = 90

FINAL ANSWER:   90

 

ENGLISH — SHORT SUMMARY

3K + 2K = 75
5K = 75
K = 15

D × K = 75
D × 15 = 75
D = 5

M = 5²
M = 25

3K + (D ÷ 1/4 + 2M) − (−5)² = ?

 

= 3(15) + (5 ÷ 1/4 + 2(25)) − 25

= 45 + (20 + 50) − 25

= 45 + 70 − 25

= 115 − 25

= 90

ANSWER: 90

Problem Author: Aris Nurdiana (Public Platform: Facebook)

Step-by-Step Solution: Akur Atan (Accuracy)

Baca versi Indonesia: Klik Di sini