Answered

Lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8.50. Ari buys 3 pounds of apples and 2 pounds of bananas for a total of $5.25. Determine a system of equations that represents the given the situation.

Verified Answer :

dexteright02

Data:
A (apple)
B (banana)

Lydia → 5A + 3B = 8.50 (I)
Ari → 3A + 2B = 5.25 (II)

Solving: System of equations that represents the given the situation.
\(\left \{ {{5A + 3B = 8.50\:(I)} \atop {3A + 2B = 5.25\:(II) }} \right.\)

Now let's find the values ​​"A" and "B", we simulated to find the value of one of the unknowns:
\(\left \{ {{5A + 3B = 8.50\:*(-2)} \atop {3A + 2B = 5.25\:*(3) }} \right.\)
\(\left \{ {{-10A -\diagup\!\!\!\!6B = -17.00} \atop {9A + \diagup\!\!\!\!6B = 15.75}} \right.\)
\(-A=-1.25\:simplify\:*(-1)\)
\(\boxed{\boxed{A=\$\:1.25}}\end{array}}\qquad\quad\checkmark\)

Now substitute one of the equations to find the value of "B":
\(5A + 3B = 8.50\:(I)\)
\(5*(1.25) + 3B = 8.50\)
\(6.25 +3B = 8.50\)
\(3B = 8.50-6.25\)
\(3B = 2.25\)
\(B = \frac{2.25}{3}\)
\(\boxed{\boxed{B = \$\:0.75}}\end{array}}\qquad\quad\checkmark\)

Answer:
Therefore, a system of equations that represents the given the situation. 
\(\boxed{\boxed{\left \{ {{5A + 3B = 8.50\:(I)} \atop {3A + 2B = 5.25\:(II) }} \right.}}\)

ardni313

Price for :

apple : $1.25

banana : $0.75

Further Explanation

One variable linear equation is an equation that has a variable and the exponent number is one.

Can be stated in the form:

\(\large {\boxed {\bold {ax = b}}\)

or

ax + b = c, where a, b, and c are constants, x is a variable

Whereas the two-variable linear equation is a linear equation that has 2 variables and the exponent is one

Can be stated in the form:

\(\large {\boxed {\bold {ax + bx = c}}}\)

x, y = variable

In this equation system there are coefficients and variables whose solutions can use:

1. substitution

2. elimination

3. graph

4. mix

Steps for completion with the substitution method:

       1. change one of the equations to the form y = ax + b or x = ay + b

2. substitution the value of x / y to another equation

         3. solve the equation

4. substitution results from point 3 in one equation


Lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $ 8.50

We express it in algebraic form

5A + 3B = 8.5 equation 1

Ari buys 3 pounds of apples and 2 pounds of bananas for a total of $ 5.25

We express it in algebraic form

3A + 2B = 5.25 equation 2

From equation 1 and 2, e use elimination and substitution

1. elimination

5A + 3B = 8.5   x 2

3A + 2B = 5.25 x 3

10A + 6B = 17

9A + 6B = 15.75

------------------------

A = 1.25

2. substitution

5A + 3B = 8.5 equation 1

5(1.25) + 3B = 8.5

B = 0.75

Learn more

the substitution method

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The work of a student to solve a set of equations

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