A jeweler had a fixed amount of gold to make bracelets and necklaces. The amount of gold in each bracelet is 6 grams and the amount of gold in each necklace is 16 grams. The jeweler used 178 grams of gold and made 7 more necklaces than bracelets. Write a system of equations that could be used to determine the number of bracelets made and the number of necklaces made. Define the variables that you use to write the system.
n = number of necklaces ... b = number of bracelets
6b + 16n = 178
n = b + 7
vibe
A summer camp is organizing a hike and needs to buy granola bars for the campers. The granola bars come in small boxes and large boxes. Each small box has 10 granola bars and each large box has 24 granola bars. The camp bought a total of 10 boxes that have 184 granola bars altogether. Write a system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased. Define the variables that you use to write the system.
Sure, here's a system of equations that could be used to determine the number of bracelets and necklaces made:
Let's assume:
B = number of bracelets made
N = number of necklaces made
The total amount of gold used is 178 grams, so the equation for gold can be written as:
6B + 16N = 178
The jeweler made 7 more necklaces than bracelets, so the equation for the number of necklaces can be written as:
N = B + 7
So the system of equations can be written as:
6B + 16N = 178
N = B + 7
These equations can be used to determine the values of B (number of bracelets) and N (number of necklaces) made.
Let's define the variables:
Let's use:
B = number of bracelets made
N = number of necklaces made
Now, let's create the system of equations:
Equation 1: The total amount of gold used in the bracelets and necklaces is 178 grams.
This can be expressed as:
6B + 16N = 178
Equation 2: The number of necklaces made is 7 more than the number of bracelets made.
This can be expressed as:
N = B + 7
So, the system of equations to determine the number of bracelets and necklaces made is:
Equation 1: 6B + 16N = 178
Equation 2: N = B + 7