Matt is five years older than twice his cousin andy’s age. the sum of their ages is less than 35.

let x represent andy's age.

which inequality represents andy’s possible age?

a.) 0< x≤25, b.) 0< x< 25, c.) 0< x< 10, d.)0< x≤10

i think it's c, am i correct?

Answer : 0<x<10

Matt is five years older than twice his cousin Andy’s age. The sum of their ages is less than 35.

Let x represent Andy's age and y represents Matt's age

Matt's age = 2*Andy's age + 5

y = 2x +5 > first equation

The sum of their ages is less than 35.

So x + y < 35

Replace y by 2x+5

x + y < 35

x + 2x + 5 < 35

3x + 5 < 35 ( subtract 5 on both sides)

3x < 30 ( divide by 3 on both sides)

x < 30

age cannot be negative . so we take x from 0 to 30

Andy’s possible age is 0<x<10

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

answer: b.

step-by-step explanation:

the y coordinate for point b is 0, and answer b is the only one with that y coordinate.