VINTAGE ANTIQUE JEWELRY

algebra 2 word problem?

A gem store sells beads made of amber and quartz. For 4 amber beads and 4 quartz beads, the cost is $46.00. For 1 amber bead and 3 quartz beads, the cost is $14.50. Find the price of each type of bead.

a=amber
b=quartz

Make a system of equations:

4a+4b=46
a+3b=14.50

Solve for each variable, I'm using substitution

a= -3b+14.50

4( -3b+14.50) +4b =46
-12b+58+4b = 46
8b+58=46
-12=8b
b= $0.66

Plug

a+3b=14.50
a+3(0.66)=14.50
a= 12.5

So if I did that right it would be $12.50 for amber, $0.66 for Quartz

Hope I helped

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