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6 September, 04:26

78% of a number, P, is 23.4 more than 117% of another number, Q. It is further given

that is 40% of P. Find P and Q.

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  1. 6 September, 04:46
    0
    Step-by-step explanation:

    "78% of P" looks like this in an algebraic expression:.78P

    "117% of Q" looks like this: 1.17Q

    " ... is 23.4 more than [above]" looks like this: [above] + 23.4

    Putting that all together in one equation, knowing that the word "is" means "equals":

    .78P = 1.17Q + 23.4

    From there, we will now use the fact that Q is 40% of P, which looks like this:

    Q =.4P

    Now, using that substitution:

    .78P = 1.17 (.4P) + 23.4 and

    .78P =.468P + 23.4 and

    .312P = 23.4 so

    P = 75

    Going back up to what Q is equal to, we will sub in the value of P and solve for Q:

    Q =.4P and P = 75, therefore,

    Q =.4 (75) so

    Q = 30
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