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(1) There are 4 more tomatoes than onions, and the sum of tomatoes and onions is 32. How many tomatoes and onions are there respectively? Use the following two ways.

[Sol 1] Let [tex]x[/tex] be the number of onions.
[tex]\[
x + (\quad) =
\][/tex]
[tex]\[
\square
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Sagot :

GinnyAnswer
Sure, let's solve this step-by-step!

[Sol 1]

1. Let [tex]\( x \)[/tex] be the number of onions.

2. There are 4 more tomatoes than onions, so the number of tomatoes can be represented as [tex]\( x + 4 \)[/tex].

3. The sum of the number of onions and tomatoes is given as 32.

So, we can write the equation as:
[tex]\[ x + (x + 4) = 32 \][/tex]

4. Simplify the equation:

[tex]\[ x + x + 4 = 32 \][/tex]

[tex]\[ 2x + 4 = 32 \][/tex]

5. Subtract 4 from both sides:

[tex]\[ 2x = 28 \][/tex]

6. Divide by 2:

[tex]\[ x = 14 \][/tex]

7. Therefore, the number of onions [tex]\( x \)[/tex] is 14.

8. The number of tomatoes is:

[tex]\[ 14 + 4 = 18 \][/tex]

Solution:
- Onions: 14
- Tomatoes: 18

### Alternative Solution

[Sol 2]

1. Let [tex]\( t \)[/tex] be the number of tomatoes.
2. Since there are 4 more tomatoes than onions, the number of onions can be represented as [tex]\( t - 4 \)[/tex].

3. The sum of the number of onions and tomatoes is given as 32.

So, we can write the equation as:
[tex]\[ (t - 4) + t = 32 \][/tex]

4. Simplify the equation:

[tex]\[ t - 4 + t = 32 \][/tex]

[tex]\[ 2t - 4 = 32 \][/tex]

5. Add 4 to both sides:

[tex]\[ 2t = 36 \][/tex]

6. Divide by 2:

[tex]\[ t = 18 \][/tex]

7. Therefore, the number of tomatoes [tex]\( t \)[/tex] is 18.

8. The number of onions is:

[tex]\[ 18 - 4 = 14 \][/tex]

Solution:
- Tomatoes: 18
- Onions: 14
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