# mahts

1)Peter claims that when a number x is increased by 10% and then decreased by 10%,

the value of x is unchanged. His calculation : x(1+10%-10%)=x Peter is wrong. Point out the mistake.

2)Find a two-digit number that satisfies the following condition:

(a) The tens-digit is greater than the unit-digit by 2.

(b)The square of the unit-digit is larger than twice the tens-digit.

A possible solution is 64. Would you suggest other solutions?

Must have step. If no step no mark will be given.

### 2 個解答

• 1 十年前
最愛解答

1.

When a number x is increased by 10%, the new value will be (1+10%) x = 1.1x

When a number y is decreased by 10%, the new value will be (1-10%) y = 0.9y

So when a number x is increased by 10% then decreased by 10%, the new value should be (1+10%) (1-10%) x = 1.1 * 0.9 x = 0.99x

The correct answer should be decreased by 1% instead of no change.

2.

Let the ten-digit be x and the unit-digit be y.

x = y + 2 ………….equation 1

y ^2 &gt; 2x =&gt; y^2 – 2x &gt; 0 …………….equation 2

Let’s substitute equation 1 into equation 2

y^2 – 2(y+2) &gt; 0

y^2 – 2y – 4 &gt; 0 …………..equation 3

From the question we know that both x and y are within the range 1 to 9. Since x = y + 2, so x must be in the range 3 to 9 while y must be in the range 1 to 7.

By substituting various value of y in the range 1 to 7 into equation 3, we note that

When y = 4, y^2 – 2y – 4 = 16 – 8 – 4 = 4 &gt;0 …. Satisfies equation 3

When y = 5, y^2 – 2y – 4 = 25 – 10 – 4 = 11 &gt;0 …. Satisfies equation 3

When y = 6, y^2 – 2y – 4 = 36 – 12 – 4 = 20 &gt;0 …. Satisfies equation 3

When y = 7, y^2 – 2y – 4 = 49 – 14 – 4 = 31 &gt;0 …. Satisfies equation 3

When y = 4, x = 6

When y = 5, x = 7

When y = 6, x = 8

When y = 7, x = 9

So the possible numbers are 64, 75, 86 and 97.

• 1 十年前

1) It is because when x increased by10%= x(1+10%)

and then decreased by 10%=1.1x(1-10%)

so the ans. should be 0.99x...not x

2)a.42

b.33