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Marta_Voda [28]
3 years ago
12

Alice's stamp collection was 75% of the size of Raymond's. After Alice sold 40% of her stamps and Raymond sold 20% of his stamps

, Alice had 140 fewer stamps than Raymond. How many stamps did Alice sell?
Mathematics
1 answer:
Maslowich3 years ago
3 0
Raymond's stamp collection ➞x
Alice′s stamp collection➞75%x
75%x-40%×75%x+140=x-20%x
75%x-30%x+140=80%x
45%x+140=80%x
140=80%x-45%x
x=400
Raymond′s stamp collection ➞400
Alice′s stamp collection➞300
Alice sold 300×40%=120
Answer:120
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r_{3}↔r_{3} - 8r_{1}

\left[\begin{array}{ccccc}1&-14&6&-9&:10\\0&7&-1&-1&:9\\0&124&-54&77&:-82\end{array}\right]

Step 3 :

r_{2}↔\frac{r_{2}}{7}

\left[\begin{array}{ccccc}1&-14&6&-9&:10\\0&1&-\frac{1}{7} &-\frac{1}{7} &:\frac{9}{7} \\0&124&-54&77&:-82\end{array}\right]

Step 4 :

r_{1}↔r_{1} + 14r_{2} , r_{3}↔r_{3} - 124r_{2}

\left[\begin{array}{ccccc}1&0&4&-11&:-8\\0&1&-\frac{1}{7} &-\frac{1}{7} &:\frac{9}{7} \\0&0&- \frac{254}{7} &\frac{663}{7} &:-\frac{1690}{7} \end{array}\right]

Step 5 :

r_{3}↔\frac{r_{3}. 7}{254}

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