Math  /  Algebra

QuestionТурийвчинд байгаа 500-тын давстарт ны 1000тын давстартазс 11-р олон. Харав 1000-тын дэвстарт х ширхэг байсан гавал 500 -тын давстартүд нийләад хадан тегрег болохыіг яаж oлох ва?

Studdy Solution

STEP 1

1. There are 500-tugrik bills and 1000-tugrik bills in the wallet.
2. The number of 1000-tugrik bills is 11 more than the number of 500-tugrik bills.
3. Let x x be the number of 1000-tugrik bills.
4. We need to find the total amount of money in the wallet in terms of x x .

STEP 2

1. Define variables for the number of 500-tugrik bills.
2. Express the relationship between the number of 500-tugrik and 1000-tugrik bills.
3. Write an equation for the total amount of money in the wallet.
4. Simplify the equation to express the total amount in terms of x x .

STEP 3

Define a variable for the number of 500-tugrik bills. Let y y be the number of 500-tugrik bills.

STEP 4

Express the relationship between the number of 500-tugrik and 1000-tugrik bills. Since the number of 1000-tugrik bills is 11 more than the number of 500-tugrik bills, we have:
x=y+11 x = y + 11

STEP 5

Write an equation for the total amount of money in the wallet. The total amount is the sum of the value of the 500-tugrik bills and the 1000-tugrik bills:
Total amount=500y+1000x \text{Total amount} = 500y + 1000x

STEP 6

Substitute the expression for y y from Step 2 into the total amount equation:
y=x11 y = x - 11
Substitute this into the total amount equation:
Total amount=500(x11)+1000x \text{Total amount} = 500(x - 11) + 1000x
Simplify the equation:
Total amount=500x5500+1000x \text{Total amount} = 500x - 5500 + 1000x Total amount=1500x5500 \text{Total amount} = 1500x - 5500
The total amount of money in the wallet in terms of x x is:
1500x5500 \boxed{1500x - 5500}

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