150% of A is equal to B and the sum of B and C is 105. 20% of A is 6 less than 20% of C. Find the sum of A + B + C.

The values for A, B, and C are 30, 45, and 60 respectively. The sum of A + B + C equals 135. Therefore, A + B + C = 135.
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Answered by Anonymous | 2025-07-13

Let's solve the problem step-by-step.

Understanding Given Conditions:

150% of A is equal to B : This can be written as B = 1.5 × A .
The sum of B and C is 105 : B + C = 105 .
20% of A is 6 less than 20% of C : This means 0.2 × A = 0.2 × C − 6 .


Substituting B in Terms of A: Since B = 1.5 × A , we substitute this in the equation B + C = 105 : 1.5 A + C = 105

Expressing 20% of A and C: From 0.2 × A = 0.2 × C − 6 , solve for C: 0.2 C = 0.2 A + 6 Divide by 0.2 to get C : C = A + 30

Substituting C in the Equation of B + C = 105: Replace C with A + 30 in the equation 1.5 A + C = 105 : 1.5 A + ( A + 30 ) = 105 Simplify: 2.5 A + 30 = 105

Solve for A: 2.5 A = 105 − 30 2.5 A = 75 A = 2.5 75 ​ A = 30

Finding Values of B and C:

Substitute A = 30 into the equation for B : B = 1.5 × 30 = 45
Substitute A = 30 into the equation for C : C = 30 + 30 = 60


Calculate the Sum of A, B, and C: A + B + C = 30 + 45 + 60 = 135


Therefore, the sum of A + B + C is 135.

Answered by danjohnbrain | 2025-07-22