P, Q, R, S and T are five consecutive integers in the increasing order. If the sum of Q, R and S is 117, what is the product of P and T?
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P, Q, R, S and T are five consecutive integers in the increasing order. If the sum of Q, R and S is 117, what is the product of P and T?
To find the product of P and T, we need to determine the values of P, Q, R, S, and T.
We are given that Q, R, and S are consecutive integers. Since they are consecutive, we can express them as follows:
Q = x
R = x + 1
S = x + 2
The sum of Q, R, and S is given to be 117, so we can write the following equation:
Q + R + S = 117
Substituting the values of Q, R, and S, we have:
x + (x + 1) + (x + 2) = 117
Combining like terms, we get:
3x + 3 = 117
Subtracting 3 from both sides, we get:
3x = 114
Dividing both sides by 3, we get:
x = 38
Now that we have determined the value of x, we can find the values of Q, R, and S:
Q = x = 38
R = x + 1 = 38 + 1 = 39
S = x + 2 = 38 + 2 = 40
We are asked to find the product of P and T. Since P and T are consecutive integers, we can express them as follows:
P = x - 2
T = x + 3
Plugging in the value of x, we get:
P = 38 - 2 = 36
T = 38 + 3 = 41
Therefore, the product of P and T is:
P * T = 36 * 41 = 1476
Hence, the product of P and T is 1476.