Fred and ethyl had 132 flowers altogether at first. After Fred sold 1/4 of his flowers and Ethyl sold 48 of her flowers, they had the same number of flowers left. How many did they each have at first?

F + E = 132
3/4 F = E - 48 ( after Fred sold 1/4 of his flowers there is 3/4 flowers left )
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E = 132 - F
3/4 F = 132 - F - 48
3/4 F + F = 84
7/4 F = 84
F = 84 : 7/4 = 84 * 4/7 = 48
E = 132 - 48 = 84
We can prove it: 3/4 * 48 = 84 - 48
36 = 36 ( correct )
Answer:
Fred had 48 flowers and Ethel 84 flowers.

Answer Link

johanrusli johanrusli · Answer 2 · 2025-04-07T09:31:04-04:00

Fred had 48 flowers.

Ethyl had 84 flowers.

Further explanation

Simultaneous Linear Equations could be solved by using several methods such as :

Elimination Method

Substitution Method

Graph Method

If we have two linear equations with 2 variables x and y , then we need to find the value of x and y that satisfying the two equations simultaneously.

Let us tackle the problem!

Let :

Number of Fred's Flowers = f

Number of Ethyl's Flowers = e

Fred and ethyl had 132 flowers altogether at first.

[tex]f + e = 132[/tex]

[tex]f = 132 - e[/tex] → Equation 1

After Fred sold 1/4 of his flowers and Ethyl sold 48 of her flowers, they had the same number of flowers left.

[tex]f - \frac{1}{4}f = e - 48[/tex]

[tex]\frac{3}{4}f = e - 48[/tex]

[tex]\frac{3}{4}(132 - e) = e - 48[/tex] ← Equation 1

[tex]\frac{3}{4}(132) - \frac{3}{4}e = e - 48[/tex]

[tex]99 + 48 = \frac{3}{4}e + e[/tex]

[tex]147 = \frac{7}{4}e[/tex]

[tex]e = 147 \div \frac{7}{4}[/tex]

[tex]e = \boxed{84}[/tex]

[tex]f = 132 - e[/tex]

[tex]f = 132 - 84[/tex]

[tex]f = \boxed {48}[/tex]

Learn more

Perimeter of Rectangle : https://brainly.com/question/12826246

Elimination Method : https://brainly.com/question/11233927

Sum of The Ages : https://brainly.com/question/11240586

Answer details

Grade: High School

Subject: Mathematics

Chapter: Simultaneous Linear Equations

Keywords: Simultaneous , Elimination , Substitution , Method , Linear , Equations