Question

How much of a spice that is 3% salt should be added to 175 ounces of a spice that is 6% salt in order to make a spice that is 5% salt?
Please Helpppp!!

Answer 1

Answer:

Let y represents the ounces of first spice.

From the given statements, we draw a table as shown below:

                          ounces of spice        Percentage          ounces of salt

First spice                 y                              3%                            0.03x

Second spice           175                            6%                          175(0.06)

Final  mixture          y + 175                         5%                        (x+15)(0.05)

Now, to solve for y

we have;

Final spice = First spice + second spice

$0.03y + 175(0.06) = (y+175)(0.05)$

$0.03y+ 10.5= 0.05y+ 8.75$

Subtract 10.5 on both sides we have;

$0.03y+ 10.5 -10.5= 0.05y+ 8.75 -10.5$

Simplify:

$0.03y = 0.05y -1.75$

Subtract 0.05y on both sides

$0.03y -0.05y= 0.05y -1.75-0.05y$

Simplify:

$-0.02y = -1.75$

Divide both sides by -0.02, we get;

$y = \frac{-1.75}{-0.02} = 87.5$

Therefore, 87.5 ounces of spices that is 3% salt should be added to 175 ounces of a spice that is 6% salt in order to make a spice that is 5% salt

Answer 2

It needs 87.5 ounces of spice that is 3% salt.

Further explanation

Order of Operations in Mathematics follow this following rule :

1. Parentheses
2. Exponents
3. Multiplication and Division
4. Addition and Subtraction

This rule is known as the PEMDAS method.

In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.

Let us tackle the problem !

$\texttt{ }$

Given:

175 ounces of a spice that is 6% salt

$\texttt{mass of salt from this spice} = s_1 = 6\% \times 175 = 10,5 \texttt{ ounces}$

$\texttt{ }$

x ounces of a spice that is 3% salt

$\texttt{mass of salt from this spice} = s_2 = 3\% \times x = 0.03x \texttt{ ounces}$

$\texttt{ }$

(175 + x) ounces of a spice that is 5% salt

$\texttt{total mass of salt} = s_1 + s_2$

$5\% \times ( 175 + x ) = 10.5 + 0.03x$

$8.75 + 0.05x = 10.5 + 0.03x$

$0.05x - 0.03x = 10.5 - 8.75$

$0.02x = 1.75$

$x = 1.75 \div 0.02$

$x = 175 \div 2$

$x = 87.5 \texttt{ ounces}$

$\texttt{ }$

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Answer details

Grade: Middle School

Subject: Mathematics

Chapter: Percentage

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent , cookies , chocolate , chip , paper , fourth , pieces , Number , 51 , 33 , 1/3