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insens350 [35]
2 years ago
14

This is a popular type of problem that appeared in mathematics textbooks in the 1970s and 1980s. can you find the answer? the su

m of the digits of a two-digit number is 6. if the digits are reversed, the difference between the new number and the original number is 18. find the original number.
Mathematics
1 answer:
kondaur [170]2 years ago
4 0
A digit is a number in one of the places, so for example the number 54 has two digits; a tens place digit (5) and a ones place digit (4).

Say the mystery number is a two digit number = xy
* that's not x times y but two side by side digits.

Info given:
<span>the sum of the digits of a two-digit number is 6
x + y = 6 </span>
<span>if the digits are reversed, yx the difference between the new number and the original number is 18.

**To obtain the number from digits you must multiply by the place and add the digits up. (Example: 54 = 10(5) + 1(4))

Original number = 10x + y
Reversed/New number = 10y + x

Difference:
10y + x - (10x + y) = 18
9y - 9x = 18
9(y - x) = 18
y - x = 18/9
y - x = 2

Now we have two equations in two variables
</span>y - x = 2
<span>x + y = 6

Re-write one in terms of one variable for substitution.
y = 2 + x
sub in to the other equation to combine them.
x + (2 + x) = 6
2x + 2 = 6
2x = 6 - 2
2x = 4
x = 2

That's the tens digit for the original number. Plug this value into either of the equations to obtain y, the ones digit.

2 + y = 6
y = 4

number "xy" = 24

</span>
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2 years ago
Douglas invests money in two simple interest accounts. He invests three times as much in an account paying 14% as he does in an
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Douglas invested $ 1300 altogether

<em><u>Solution:</u></em>

Let x represent the amount invested in the account paying 14% interest.

Let y represent the amount invested in the account paying 5% interest

He invests three times as much in an account paying 14% as he does in an account paying 5%

Which means,

x = 3y

<em><u>The simple interest is given by formula:</u></em>

S.I = \frac{p \times n \times r}{100}

Where,

"p" is the principal

"n" is the number of years

"r" is the rate of interest

<em><u>He earns $152.75 in interest in one year from both accounts combined</u></em>

Therefore,

Combined S.I = 152.75

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<em><u>Considering the account earning 14% interest:</u></em>

S.I = \frac{3y \times 14 \times 1}{100}\\\\S.I = 0.42y

<em><u>Considering the account earning 5% interest:</u></em>

S.I = \frac{y \times 5 \times 1}{100}\\\\S.I = 0.05y

<em><u>Since, Combined S.I = 152.75</u></em>

Therefore,

0.42y + 0.05y = 152.75

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Divide both sides by 0.47

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<em><u>how much did he invest altogether?</u></em>

Amount invested together = x + y = 975 + 325 = 1300

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45 / 3 = 1 Ticket

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